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

Percentage Accurate: 98.5% → 98.5%

Time: 22.0s

Alternatives: 22

Speedup: 1.0×

• 46.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

3. Final simplification 97.5%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+27} \lor \neg \left(y \leq 58000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.02e+27) (not (<= y 58000.0)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) 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 <= -1.02e+27) || !(y <= 58000.0)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 <= (-1.02d+27)) .or. (.not. (y <= 58000.0d0))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 <= -1.02e+27) || !(y <= 58000.0)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / 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 <= -1.02e+27) or not (y <= 58000.0):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / 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 <= -1.02e+27) || !(y <= 58000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / 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 <= -1.02e+27) || ~((y <= 58000.0)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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, -1.02e+27], N[Not[LessEqual[y, 58000.0]], $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], 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 < -1.0199999999999999e27 or 58000 < 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 t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   if -1.0199999999999999e27 < y < 58000

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 95.3%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+27} \lor \neg \left(y \leq 58000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+28} \lor \neg \left(y \leq 57000000\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+28) (not (<= y 57000000.0)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+28) || !(y <= 57000000.0)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d+28)) .or. (.not. (y <= 57000000.0d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+28) || !(y <= 57000000.0)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+28) or not (y <= 57000000.0):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+28) || !(y <= 57000000.0))
		tmp = Float64(Float64(x * Float64((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 <= -1.05e+28) || ~((y <= 57000000.0)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+28], N[Not[LessEqual[y, 57000000.0]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $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 < -1.04999999999999995e28 or 5.7e7 < 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 t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in b around 0 85.9%

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

      1. div-exp 85.9%

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

      2. *-commutative 85.9%

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

      3. exp-to-pow 85.9%

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

      4. rem-exp-log 85.9%

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

   8. Simplified 85.9%

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

   if -1.04999999999999995e28 < y < 5.7e7

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 95.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+28} \lor \neg \left(y \leq 57000000\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90000 \lor \neg \left(y \leq 86\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -90000.0) (not (<= y 86.0)))
   (/ (* x (/ (pow z y) a)) y)
   (* x (/ (/ (pow a t) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -90000.0) || !(y <= 86.0)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * ((pow(a, t) / a) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-90000.0d0)) .or. (.not. (y <= 86.0d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x * (((a ** t) / a) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -90000.0) || !(y <= 86.0)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x * ((Math.pow(a, t) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -90000.0) or not (y <= 86.0):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x * ((math.pow(a, t) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -90000.0) || !(y <= 86.0))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -90000.0) || ~((y <= 86.0)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x * (((a ^ t) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -90000.0], N[Not[LessEqual[y, 86.0]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e4 or 86 < 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 t around 0 92.8%

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

      1. +-commutative 92.8%

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

      2. mul-1-neg 92.8%

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

      3. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in b around 0 84.8%

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

      1. div-exp 84.8%

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

      2. *-commutative 84.8%

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

      3. exp-to-pow 84.8%

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

      4. rem-exp-log 84.8%

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

   8. Simplified 84.8%

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

   if -9e4 < y < 86

   1. Initial program 95.6%

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

      1. associate-/l* 97.9%

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

      2. associate--l+ 97.9%

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

      3. exp-sum 97.9%

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

      4. associate-/l* 97.9%

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

      5. *-commutative 97.9%

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

      6. exp-to-pow 97.9%

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

      7. exp-diff 88.3%

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

      8. *-commutative 88.3%

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

      9. exp-to-pow 89.6%

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

      10. sub-neg 89.6%

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

      11. metadata-eval 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around 0 87.9%

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

      1. exp-to-pow 89.0%

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

      2. sub-neg 89.0%

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

      3. metadata-eval 89.0%

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

   7. Simplified 89.0%

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

      1. unpow-prod-up 65.3%

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

      2. unpow-1 65.3%

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

   9. Applied egg-rr 89.2%

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

       1. associate-*r/ 65.3%

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

       2. *-rgt-identity 65.3%

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

   11. Simplified 89.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90000 \lor \neg \left(y \leq 86\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1600000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -1.5e+26)
     t_2
     (if (<= y 1.85e-193)
       t_1
       (if (<= y 1.1e-148)
         (* (/ (pow a t) a) (/ x y))
         (if (<= y 1600000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.5e+26) {
		tmp = t_2;
	} else if (y <= 1.85e-193) {
		tmp = t_1;
	} else if (y <= 1.1e-148) {
		tmp = (pow(a, t) / a) * (x / y);
	} else if (y <= 1600000.0) {
		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 * exp(b))) / y
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-1.5d+26)) then
        tmp = t_2
    else if (y <= 1.85d-193) then
        tmp = t_1
    else if (y <= 1.1d-148) then
        tmp = ((a ** t) / a) * (x / y)
    else if (y <= 1600000.0d0) 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 / (a * Math.exp(b))) / y;
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.5e+26) {
		tmp = t_2;
	} else if (y <= 1.85e-193) {
		tmp = t_1;
	} else if (y <= 1.1e-148) {
		tmp = (Math.pow(a, t) / a) * (x / y);
	} else if (y <= 1600000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -1.5e+26:
		tmp = t_2
	elif y <= 1.85e-193:
		tmp = t_1
	elif y <= 1.1e-148:
		tmp = (math.pow(a, t) / a) * (x / y)
	elif y <= 1600000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -1.5e+26)
		tmp = t_2;
	elseif (y <= 1.85e-193)
		tmp = t_1;
	elseif (y <= 1.1e-148)
		tmp = Float64(Float64((a ^ t) / a) * Float64(x / y));
	elseif (y <= 1600000.0)
		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 * exp(b))) / y;
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -1.5e+26)
		tmp = t_2;
	elseif (y <= 1.85e-193)
		tmp = t_1;
	elseif (y <= 1.1e-148)
		tmp = ((a ^ t) / a) * (x / y);
	elseif (y <= 1600000.0)
		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[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.5e+26], t$95$2, If[LessEqual[y, 1.85e-193], t$95$1, If[LessEqual[y, 1.1e-148], N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1600000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999999e26 or 1.6e6 < 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 t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in b around 0 85.9%

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

      1. div-exp 85.9%

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

      2. *-commutative 85.9%

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

      3. exp-to-pow 85.9%

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

      4. rem-exp-log 85.9%

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

   8. Simplified 85.9%

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

   if -1.49999999999999999e26 < y < 1.8500000000000001e-193 or 1.10000000000000009e-148 < y < 1.6e6

   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 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around 0 82.9%

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

      1. exp-neg 82.9%

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

      2. associate-*r/ 82.9%

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

      3. *-rgt-identity 82.9%

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

      4. +-commutative 82.9%

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

      5. exp-sum 82.9%

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

      6. rem-exp-log 83.9%

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

   8. Simplified 83.9%

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

   if 1.8500000000000001e-193 < y < 1.10000000000000009e-148

   1. Initial program 80.5%

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

      1. associate-/l* 97.7%

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

      2. associate--l+ 97.7%

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

      3. exp-sum 97.7%

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

      4. associate-/l* 97.7%

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

      5. *-commutative 97.7%

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

      6. exp-to-pow 97.7%

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

      7. exp-diff 90.6%

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

      8. *-commutative 90.6%

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

      9. exp-to-pow 92.7%

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

      10. sub-neg 92.7%

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

      11. metadata-eval 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. *-commutative 73.4%

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

      3. times-frac 90.6%

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

      4. exp-to-pow 92.7%

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

      5. sub-neg 92.7%

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

      6. metadata-eval 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in b around 0 83.8%

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

      1. exp-to-pow 86.0%

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

      2. sub-neg 86.0%

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

      3. metadata-eval 86.0%

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

   10. Simplified 86.0%

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

       1. unpow-prod-up 86.0%

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

       2. unpow-1 86.0%

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

   12. Applied egg-rr 86.0%

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

       1. associate-*r/ 86.0%

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

       2. *-rgt-identity 86.0%

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

   14. Simplified 86.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-193}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1600000:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (exp b) (* y a)))))
   (if (<= b -3.7e-67)
     t_1
     (if (<= b 8.5e+14)
       (/ x (* b (* a (+ y (/ y b)))))
       (if (<= b 8.6e+135)
         t_1
         (/
          x
          (*
           a
           (+
            y
            (*
             b
             (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (exp(b) * (y * a));
	double tmp;
	if (b <= -3.7e-67) {
		tmp = t_1;
	} else if (b <= 8.5e+14) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 8.6e+135) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (exp(b) * (y * a))
    if (b <= (-3.7d-67)) then
        tmp = t_1
    else if (b <= 8.5d+14) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 8.6d+135) then
        tmp = t_1
    else
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (Math.exp(b) * (y * a));
	double tmp;
	if (b <= -3.7e-67) {
		tmp = t_1;
	} else if (b <= 8.5e+14) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 8.6e+135) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (math.exp(b) * (y * a))
	tmp = 0
	if b <= -3.7e-67:
		tmp = t_1
	elif b <= 8.5e+14:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 8.6e+135:
		tmp = t_1
	else:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(exp(b) * Float64(y * a)))
	tmp = 0.0
	if (b <= -3.7e-67)
		tmp = t_1;
	elseif (b <= 8.5e+14)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 8.6e+135)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (exp(b) * (y * a));
	tmp = 0.0;
	if (b <= -3.7e-67)
		tmp = t_1;
	elseif (b <= 8.5e+14)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 8.6e+135)
		tmp = t_1;
	else
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e-67], t$95$1, If[LessEqual[b, 8.5e+14], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+135], t$95$1, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.6999999999999999e-67 or 8.5e14 < b < 8.59999999999999945e135

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0 76.1%

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

      1. associate-/l* 75.2%

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

      2. exp-neg 75.2%

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

      3. exp-sum 75.2%

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

      4. rem-exp-log 75.3%

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

      5. associate-/l/ 75.3%

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

      6. associate-/r* 75.3%

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

      7. *-commutative 75.3%

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

      8. associate-/r* 75.3%

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

      9. associate-/l* 75.3%

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

      10. *-rgt-identity 75.3%

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

      11. associate-*r* 71.4%

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

      12. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   if -3.6999999999999999e-67 < b < 8.5e14

   1. Initial program 94.6%

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

   3. Taylor expanded in t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around 0 39.6%

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

      1. associate-/l* 43.3%

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

      2. exp-neg 43.3%

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

      3. exp-sum 43.3%

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

      4. rem-exp-log 44.7%

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

      5. associate-/l/ 44.7%

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

      6. associate-/r* 44.6%

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

      7. *-commutative 44.6%

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

      8. associate-/r* 45.4%

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

      9. associate-/l* 45.5%

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

      10. *-rgt-identity 45.5%

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

      11. associate-*r* 45.5%

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

      12. *-commutative 45.5%

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

   8. Simplified 45.5%

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

   9. Taylor expanded in b around 0 42.9%

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

       1. distribute-lft-out 45.5%

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

       2. distribute-rgt1-in 45.5%

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

   11. Simplified 45.5%

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

   12. Taylor expanded in b around inf 41.0%

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

       1. associate-/l* 50.2%

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

       2. distribute-lft-out 55.4%

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

   14. Simplified 55.4%

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

   if 8.59999999999999945e135 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.1%

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

      1. associate-/l* 89.1%

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

      2. exp-neg 89.1%

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

      3. exp-sum 89.1%

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

      4. rem-exp-log 89.1%

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

      5. associate-/l/ 89.1%

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

      6. associate-/r* 89.1%

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

      7. *-commutative 89.1%

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

      8. associate-/r* 89.1%

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

      9. associate-/l* 89.1%

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

      10. *-rgt-identity 89.1%

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

      11. associate-*r* 66.8%

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

      12. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   9. Taylor expanded in b around 0 72.8%

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

   10. Taylor expanded in a around 0 86.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+135}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.82 \cdot 10^{+59} \lor \neg \left(b \leq 4.1 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.82e+59) (not (<= b 4.1e+43)))
   (/ (/ x (* a (exp b))) y)
   (* x (/ (pow z y) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.82e+59) || !(b <= 4.1e+43)) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = x * (pow(z, y) / (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 <= (-1.82d+59)) .or. (.not. (b <= 4.1d+43))) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = x * ((z ** y) / (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 <= -1.82e+59) || !(b <= 4.1e+43)) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = x * (Math.pow(z, y) / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.82e+59) or not (b <= 4.1e+43):
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = x * (math.pow(z, y) / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.82e+59) || !(b <= 4.1e+43))
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = Float64(x * Float64((z ^ y) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.82e+59) || ~((b <= 4.1e+43)))
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = x * ((z ^ y) / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.82e+59], N[Not[LessEqual[b, 4.1e+43]], $MachinePrecision]], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.82000000000000008e59 or 4.1e43 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 95.4%

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

      1. +-commutative 95.4%

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

      2. mul-1-neg 95.4%

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

      3. unsub-neg 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in y around 0 87.2%

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

      1. exp-neg 87.2%

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

      2. associate-*r/ 87.2%

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

      3. *-rgt-identity 87.2%

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

      4. +-commutative 87.2%

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

      5. exp-sum 87.2%

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

      6. rem-exp-log 87.2%

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

   8. Simplified 87.2%

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

   if -1.82000000000000008e59 < b < 4.1e43

   1. Initial program 95.6%

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

      1. associate-/l* 97.9%

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

      2. associate--l+ 97.9%

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

      3. exp-sum 84.4%

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

      4. associate-/l* 83.7%

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

      5. *-commutative 83.7%

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

      6. exp-to-pow 83.7%

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

      7. exp-diff 80.3%

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

      8. *-commutative 80.3%

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

      9. exp-to-pow 81.6%

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

      10. sub-neg 81.6%

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

      11. metadata-eval 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in b around 0 82.5%

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

      1. associate-/l* 82.5%

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

      2. exp-to-pow 83.7%

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

      3. sub-neg 83.7%

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

      4. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in t around 0 74.4%

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

      1. *-commutative 74.4%

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

   10. Simplified 74.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.82 \cdot 10^{+59} \lor \neg \left(b \leq 4.1 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-75} \lor \neg \left(b \leq 8.5 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e-75) (not (<= b 8.5e+14)))
   (/ (/ x (* a (exp b))) y)
   (/ x (* b (* a (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-75) || !(b <= 8.5e+14)) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.5d-75)) .or. (.not. (b <= 8.5d+14))) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = x / (b * (a * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-75) || !(b <= 8.5e+14)) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.5e-75) or not (b <= 8.5e+14):
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = x / (b * (a * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e-75) || !(b <= 8.5e+14))
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.5e-75) || ~((b <= 8.5e+14)))
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = x / (b * (a * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e-75], N[Not[LessEqual[b, 8.5e+14]], $MachinePrecision]], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4999999999999999e-75 or 8.5e14 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. mul-1-neg 91.4%

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

      3. unsub-neg 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around 0 78.9%

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

      1. exp-neg 78.9%

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

      2. associate-*r/ 78.9%

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

      3. *-rgt-identity 78.9%

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

      4. +-commutative 78.9%

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

      5. exp-sum 78.9%

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

      6. rem-exp-log 79.0%

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

   8. Simplified 79.0%

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

   if -1.4999999999999999e-75 < b < 8.5e14

   1. Initial program 94.6%

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

   3. Taylor expanded in t around 0 77.2%

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

      1. +-commutative 77.2%

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

      2. mul-1-neg 77.2%

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

      3. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in y around 0 39.8%

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

      1. associate-/l* 43.6%

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

      2. exp-neg 43.6%

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

      3. exp-sum 43.6%

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

      4. rem-exp-log 45.0%

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

      5. associate-/l/ 45.0%

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

      6. associate-/r* 45.0%

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

      7. *-commutative 45.0%

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

      8. associate-/r* 45.7%

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

      9. associate-/l* 45.8%

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

      10. *-rgt-identity 45.8%

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

      11. associate-*r* 45.8%

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

      12. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   9. Taylor expanded in b around 0 43.2%

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

       1. distribute-lft-out 45.8%

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

       2. distribute-rgt1-in 45.8%

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

   11. Simplified 45.8%

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

   12. Taylor expanded in b around inf 41.3%

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

       1. associate-/l* 50.6%

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

       2. distribute-lft-out 55.8%

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

   14. Simplified 55.8%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-75} \lor \neg \left(b \leq 8.5 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.0% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;t\_1 - b \cdot \left(t\_1 - b \cdot \left(t\_1 - \frac{x \cdot b}{y \cdot a}\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -2.7e-62)
     (- t_1 (* b (- t_1 (* b (- t_1 (/ (* x b) (* y a)))))))
     (if (<= b 3.2e+93)
       (/ x (* b (* a (+ y (/ y b)))))
       (/
        x
        (*
         y
         (+
          a
          (*
           b
           (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -2.7e-62) {
		tmp = t_1 - (b * (t_1 - (b * (t_1 - ((x * b) / (y * a))))));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-2.7d-62)) then
        tmp = t_1 - (b * (t_1 - (b * (t_1 - ((x * b) / (y * a))))))
    else if (b <= 3.2d+93) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -2.7e-62) {
		tmp = t_1 - (b * (t_1 - (b * (t_1 - ((x * b) / (y * a))))));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -2.7e-62:
		tmp = t_1 - (b * (t_1 - (b * (t_1 - ((x * b) / (y * a))))))
	elif b <= 3.2e+93:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -2.7e-62)
		tmp = Float64(t_1 - Float64(b * Float64(t_1 - Float64(b * Float64(t_1 - Float64(Float64(x * b) / Float64(y * a)))))));
	elseif (b <= 3.2e+93)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -2.7e-62)
		tmp = t_1 - (b * (t_1 - (b * (t_1 - ((x * b) / (y * a))))));
	elseif (b <= 3.2e+93)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e-62], N[(t$95$1 - N[(b * N[(t$95$1 - N[(b * N[(t$95$1 - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+93], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.70000000000000019e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 77.9%

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

      2. exp-neg 77.9%

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

      3. exp-sum 77.9%

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

      4. rem-exp-log 77.9%

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

      5. associate-/l/ 77.9%

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

      6. associate-/r* 77.9%

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

      7. *-commutative 77.9%

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

      8. associate-/r* 77.9%

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

      9. associate-/l* 77.9%

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

      10. *-rgt-identity 77.9%

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

      11. associate-*r* 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in b around 0 14.1%

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

       1. distribute-lft-out 14.2%

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

       2. distribute-rgt1-in 14.2%

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

   11. Simplified 14.2%

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

   12. Taylor expanded in b around 0 62.8%

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

   if -2.70000000000000019e-62 < b < 3.2000000000000001e93

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 41.7%

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

      1. associate-/l* 44.9%

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

      2. exp-neg 44.9%

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

      3. exp-sum 44.9%

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

      4. rem-exp-log 46.1%

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

      5. associate-/l/ 46.1%

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

      6. associate-/r* 46.1%

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

      7. *-commutative 46.1%

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

      8. associate-/r* 46.8%

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

      9. associate-/l* 46.9%

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

      10. *-rgt-identity 46.9%

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

      11. associate-*r* 46.9%

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

      12. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in b around 0 42.5%

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

       1. distribute-lft-out 44.7%

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

       2. distribute-rgt1-in 44.7%

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

   11. Simplified 44.7%

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

   12. Taylor expanded in b around inf 40.9%

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

       1. associate-/l* 48.8%

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

       2. distribute-lft-out 53.3%

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

   14. Simplified 53.3%

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

   if 3.2000000000000001e93 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. exp-neg 89.3%

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

      3. exp-sum 89.3%

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

      4. rem-exp-log 89.3%

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

      5. associate-/l/ 89.3%

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

      6. associate-/r* 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-/r* 89.3%

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

      9. associate-/l* 89.3%

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

      10. *-rgt-identity 89.3%

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

      11. associate-*r* 71.9%

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

      12. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in b around 0 70.2%

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

   10. Taylor expanded in y around 0 80.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \left(\frac{x}{y \cdot a} - b \cdot \left(\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.8% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;t\_1 - b \cdot \left(t\_1 - \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -1.55e-62)
     (- t_1 (* b (- t_1 (/ (* x b) (* y a)))))
     (if (<= b 3.8e+93)
       (/ x (* b (* a (+ y (/ y b)))))
       (/
        x
        (*
         a
         (+
          y
          (*
           b
           (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -1.55e-62) {
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	} else if (b <= 3.8e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-1.55d-62)) then
        tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))))
    else if (b <= 3.8d+93) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -1.55e-62) {
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	} else if (b <= 3.8e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -1.55e-62:
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))))
	elif b <= 3.8e+93:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -1.55e-62)
		tmp = Float64(t_1 - Float64(b * Float64(t_1 - Float64(Float64(x * b) / Float64(y * a)))));
	elseif (b <= 3.8e+93)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -1.55e-62)
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	elseif (b <= 3.8e+93)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e-62], N[(t$95$1 - N[(b * N[(t$95$1 - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+93], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.55e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 77.9%

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

      2. exp-neg 77.9%

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

      3. exp-sum 77.9%

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

      4. rem-exp-log 77.9%

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

      5. associate-/l/ 77.9%

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

      6. associate-/r* 77.9%

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

      7. *-commutative 77.9%

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

      8. associate-/r* 77.9%

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

      9. associate-/l* 77.9%

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

      10. *-rgt-identity 77.9%

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

      11. associate-*r* 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in b around 0 14.1%

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

       1. distribute-lft-out 14.2%

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

       2. distribute-rgt1-in 14.2%

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

   11. Simplified 14.2%

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

   12. Taylor expanded in b around 0 57.7%

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

   if -1.55e-62 < b < 3.7999999999999998e93

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 41.7%

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

      1. associate-/l* 44.9%

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

      2. exp-neg 44.9%

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

      3. exp-sum 44.9%

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

      4. rem-exp-log 46.1%

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

      5. associate-/l/ 46.1%

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

      6. associate-/r* 46.1%

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

      7. *-commutative 46.1%

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

      8. associate-/r* 46.8%

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

      9. associate-/l* 46.9%

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

      10. *-rgt-identity 46.9%

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

      11. associate-*r* 46.9%

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

      12. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in b around 0 42.5%

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

       1. distribute-lft-out 44.7%

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

       2. distribute-rgt1-in 44.7%

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

   11. Simplified 44.7%

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

   12. Taylor expanded in b around inf 40.9%

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

       1. associate-/l* 48.8%

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

       2. distribute-lft-out 53.3%

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

   14. Simplified 53.3%

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

   if 3.7999999999999998e93 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. exp-neg 89.3%

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

      3. exp-sum 89.3%

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

      4. rem-exp-log 89.3%

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

      5. associate-/l/ 89.3%

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

      6. associate-/r* 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-/r* 89.3%

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

      9. associate-/l* 89.3%

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

      10. *-rgt-identity 89.3%

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

      11. associate-*r* 71.9%

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

      12. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in b around 0 70.2%

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

   10. Taylor expanded in a around 0 80.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \left(\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;t\_1 - b \cdot \left(t\_1 - \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -1.55e-62)
     (- t_1 (* b (- t_1 (/ (* x b) (* y a)))))
     (if (<= b 3.2e+93)
       (/ x (* b (* a (+ y (/ y b)))))
       (/
        x
        (*
         y
         (+
          a
          (*
           b
           (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -1.55e-62) {
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-1.55d-62)) then
        tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))))
    else if (b <= 3.2d+93) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -1.55e-62) {
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -1.55e-62:
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))))
	elif b <= 3.2e+93:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -1.55e-62)
		tmp = Float64(t_1 - Float64(b * Float64(t_1 - Float64(Float64(x * b) / Float64(y * a)))));
	elseif (b <= 3.2e+93)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -1.55e-62)
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	elseif (b <= 3.2e+93)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e-62], N[(t$95$1 - N[(b * N[(t$95$1 - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+93], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.55e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 77.9%

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

      2. exp-neg 77.9%

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

      3. exp-sum 77.9%

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

      4. rem-exp-log 77.9%

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

      5. associate-/l/ 77.9%

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

      6. associate-/r* 77.9%

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

      7. *-commutative 77.9%

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

      8. associate-/r* 77.9%

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

      9. associate-/l* 77.9%

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

      10. *-rgt-identity 77.9%

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

      11. associate-*r* 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in b around 0 14.1%

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

       1. distribute-lft-out 14.2%

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

       2. distribute-rgt1-in 14.2%

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

   11. Simplified 14.2%

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

   12. Taylor expanded in b around 0 57.7%

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

   if -1.55e-62 < b < 3.2000000000000001e93

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 41.7%

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

      1. associate-/l* 44.9%

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

      2. exp-neg 44.9%

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

      3. exp-sum 44.9%

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

      4. rem-exp-log 46.1%

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

      5. associate-/l/ 46.1%

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

      6. associate-/r* 46.1%

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

      7. *-commutative 46.1%

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

      8. associate-/r* 46.8%

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

      9. associate-/l* 46.9%

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

      10. *-rgt-identity 46.9%

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

      11. associate-*r* 46.9%

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

      12. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in b around 0 42.5%

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

       1. distribute-lft-out 44.7%

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

       2. distribute-rgt1-in 44.7%

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

   11. Simplified 44.7%

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

   12. Taylor expanded in b around inf 40.9%

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

       1. associate-/l* 48.8%

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

       2. distribute-lft-out 53.3%

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

   14. Simplified 53.3%

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

   if 3.2000000000000001e93 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. exp-neg 89.3%

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

      3. exp-sum 89.3%

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

      4. rem-exp-log 89.3%

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

      5. associate-/l/ 89.3%

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

      6. associate-/r* 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-/r* 89.3%

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

      9. associate-/l* 89.3%

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

      10. *-rgt-identity 89.3%

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

      11. associate-*r* 71.9%

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

      12. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in b around 0 70.2%

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

   10. Taylor expanded in y around 0 80.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \left(\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.4% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + 0.5 \cdot \left(a \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8e-91)
   (- (/ x (* y a)) (/ (* x b) (* y a)))
   (if (<= b 3.2e+93)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ x (+ (* y a) (* b (+ (* y a) (* 0.5 (* a (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e-91) {
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8d-91)) then
        tmp = (x / (y * a)) - ((x * b) / (y * a))
    else if (b <= 3.2d+93) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / ((y * a) + (b * ((y * a) + (0.5d0 * (a * (y * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e-91) {
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8e-91:
		tmp = (x / (y * a)) - ((x * b) / (y * a))
	elif b <= 3.2e+93:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8e-91)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x * b) / Float64(y * a)));
	elseif (b <= 3.2e+93)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * a) + Float64(0.5 * Float64(a * Float64(y * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8e-91)
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	elseif (b <= 3.2e+93)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8e-91], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+93], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * a), $MachinePrecision] + N[(0.5 * N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.00000000000000018e-91

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

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

      3. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in y around 0 74.5%

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

      1. associate-/l* 73.4%

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

      2. exp-neg 73.4%

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

      3. exp-sum 73.4%

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

      4. rem-exp-log 73.5%

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

      5. associate-/l/ 73.5%

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

      6. associate-/r* 73.5%

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

      7. *-commutative 73.5%

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

      8. associate-/r* 74.6%

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

      9. associate-/l* 74.6%

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

      10. *-rgt-identity 74.6%

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

      11. associate-*r* 69.8%

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

      12. *-commutative 69.8%

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

   8. Simplified 69.8%

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

   9. Taylor expanded in b around 0 44.2%

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

   if -8.00000000000000018e-91 < b < 3.2000000000000001e93

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in y around 0 42.2%

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

      1. associate-/l* 45.6%

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

      2. exp-neg 45.6%

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

      3. exp-sum 45.6%

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

      4. rem-exp-log 46.9%

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

      5. associate-/l/ 46.9%

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

      6. associate-/r* 46.9%

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

      7. *-commutative 46.9%

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

      8. associate-/r* 46.9%

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

      9. associate-/l* 46.9%

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

      10. *-rgt-identity 46.9%

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

      11. associate-*r* 46.9%

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

      12. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in b around 0 42.2%

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

       1. distribute-lft-out 44.6%

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

       2. distribute-rgt1-in 44.6%

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

   11. Simplified 44.6%

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

   12. Taylor expanded in b around inf 41.3%

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

       1. associate-/l* 49.8%

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

       2. distribute-lft-out 53.8%

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

   14. Simplified 53.8%

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

   if 3.2000000000000001e93 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. exp-neg 89.3%

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

      3. exp-sum 89.3%

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

      4. rem-exp-log 89.3%

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

      5. associate-/l/ 89.3%

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

      6. associate-/r* 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-/r* 89.3%

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

      9. associate-/l* 89.3%

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

      10. *-rgt-identity 89.3%

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

      11. associate-*r* 71.9%

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

      12. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in b around 0 53.7%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + 0.5 \cdot \left(a \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.8% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;t\_1 - b \cdot \left(t\_1 - \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + 0.5 \cdot \left(a \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -2.5e-62)
     (- t_1 (* b (- t_1 (/ (* x b) (* y a)))))
     (if (<= b 3.2e+93)
       (/ x (* b (* a (+ y (/ y b)))))
       (/ x (+ (* y a) (* b (+ (* y a) (* 0.5 (* a (* y b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -2.5e-62) {
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-2.5d-62)) then
        tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))))
    else if (b <= 3.2d+93) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / ((y * a) + (b * ((y * a) + (0.5d0 * (a * (y * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -2.5e-62) {
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	} else if (b <= 3.2e+93) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -2.5e-62:
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))))
	elif b <= 3.2e+93:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -2.5e-62)
		tmp = Float64(t_1 - Float64(b * Float64(t_1 - Float64(Float64(x * b) / Float64(y * a)))));
	elseif (b <= 3.2e+93)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * a) + Float64(0.5 * Float64(a * Float64(y * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -2.5e-62)
		tmp = t_1 - (b * (t_1 - ((x * b) / (y * a))));
	elseif (b <= 3.2e+93)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / ((y * a) + (b * ((y * a) + (0.5 * (a * (y * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e-62], N[(t$95$1 - N[(b * N[(t$95$1 - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+93], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * a), $MachinePrecision] + N[(0.5 * N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5000000000000001e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 77.9%

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

      2. exp-neg 77.9%

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

      3. exp-sum 77.9%

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

      4. rem-exp-log 77.9%

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

      5. associate-/l/ 77.9%

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

      6. associate-/r* 77.9%

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

      7. *-commutative 77.9%

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

      8. associate-/r* 77.9%

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

      9. associate-/l* 77.9%

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

      10. *-rgt-identity 77.9%

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

      11. associate-*r* 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in b around 0 14.1%

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

       1. distribute-lft-out 14.2%

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

       2. distribute-rgt1-in 14.2%

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

   11. Simplified 14.2%

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

   12. Taylor expanded in b around 0 57.7%

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

   if -2.5000000000000001e-62 < b < 3.2000000000000001e93

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 41.7%

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

      1. associate-/l* 44.9%

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

      2. exp-neg 44.9%

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

      3. exp-sum 44.9%

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

      4. rem-exp-log 46.1%

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

      5. associate-/l/ 46.1%

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

      6. associate-/r* 46.1%

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

      7. *-commutative 46.1%

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

      8. associate-/r* 46.8%

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

      9. associate-/l* 46.9%

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

      10. *-rgt-identity 46.9%

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

      11. associate-*r* 46.9%

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

      12. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in b around 0 42.5%

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

       1. distribute-lft-out 44.7%

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

       2. distribute-rgt1-in 44.7%

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

   11. Simplified 44.7%

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

   12. Taylor expanded in b around inf 40.9%

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

       1. associate-/l* 48.8%

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

       2. distribute-lft-out 53.3%

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

   14. Simplified 53.3%

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

   if 3.2000000000000001e93 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. associate-/l* 89.3%

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

      2. exp-neg 89.3%

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

      3. exp-sum 89.3%

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

      4. rem-exp-log 89.3%

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

      5. associate-/l/ 89.3%

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

      6. associate-/r* 89.3%

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

      7. *-commutative 89.3%

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

      8. associate-/r* 89.3%

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

      9. associate-/l* 89.3%

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

      10. *-rgt-identity 89.3%

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

      11. associate-*r* 71.9%

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

      12. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in b around 0 53.7%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \left(\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + 0.5 \cdot \left(a \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e-62)
   (* (/ x (* y a)) (- (- -1.0) b))
   (if (<= b 4e+117) (/ x (* b (* a (+ y (/ y b))))) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-62) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else if (b <= 4e+117) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d-62)) then
        tmp = (x / (y * a)) * (-(-1.0d0) - b)
    else if (b <= 4d+117) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-62) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else if (b <= 4e+117) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e-62:
		tmp = (x / (y * a)) * (-(-1.0) - b)
	elif b <= 4e+117:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e-62)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(Float64(-(-1.0)) - b));
	elseif (b <= 4e+117)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e-62)
		tmp = (x / (y * a)) * (-(-1.0) - b);
	elseif (b <= 4e+117)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e-62], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+117], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.0000000000000001e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 77.9%

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

      2. exp-neg 77.9%

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

      3. exp-sum 77.9%

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

      4. rem-exp-log 77.9%

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

      5. associate-/l/ 77.9%

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

      6. associate-/r* 77.9%

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

      7. *-commutative 77.9%

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

      8. associate-/r* 77.9%

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

      9. associate-/l* 77.9%

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

      10. *-rgt-identity 77.9%

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

      11. associate-*r* 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in b around 0 14.1%

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

       1. distribute-lft-out 14.2%

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

       2. distribute-rgt1-in 14.2%

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

   11. Simplified 14.2%

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

   12. Taylor expanded in b around 0 43.9%

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

       1. mul-1-neg 43.9%

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

       2. remove-double-neg 43.9%

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

       3. distribute-neg-out 43.9%

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

       4. associate-/l* 41.5%

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

       5. mul-1-neg 41.5%

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

       6. distribute-rgt-out 41.5%

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

       7. *-commutative 41.5%

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

   14. Simplified 41.5%

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

   if -2.0000000000000001e-62 < b < 4.0000000000000002e117

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in y around 0 44.3%

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

      1. associate-/l* 47.3%

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

      2. exp-neg 47.4%

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

      3. exp-sum 47.4%

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

      4. rem-exp-log 48.5%

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

      5. associate-/l/ 48.5%

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

      6. associate-/r* 48.5%

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

      7. *-commutative 48.5%

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

      8. associate-/r* 49.1%

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

      9. associate-/l* 49.2%

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

      10. *-rgt-identity 49.2%

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

      11. associate-*r* 49.2%

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

      12. *-commutative 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in b around 0 42.3%

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

       1. distribute-lft-out 44.4%

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

       2. distribute-rgt1-in 44.4%

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

   11. Simplified 44.4%

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

   12. Taylor expanded in b around inf 40.8%

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

       1. associate-/l* 48.3%

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

       2. distribute-lft-out 52.5%

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

   14. Simplified 52.5%

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

   if 4.0000000000000002e117 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.6%

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

      1. associate-/l* 89.6%

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

      2. exp-neg 89.6%

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

      3. exp-sum 89.6%

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

      4. rem-exp-log 89.6%

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

      5. associate-/l/ 89.6%

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

      6. associate-/r* 89.6%

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

      7. *-commutative 89.6%

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

      8. associate-/r* 89.6%

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

      9. associate-/l* 89.6%

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

      10. *-rgt-identity 89.6%

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

      11. associate-*r* 68.6%

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

      12. *-commutative 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in b around 0 33.6%

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

       1. distribute-lft-out 33.6%

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

       2. distribute-rgt1-in 33.6%

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

   11. Simplified 33.6%

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

   12. Taylor expanded in b around inf 33.6%

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

       1. associate-*r* 38.8%

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

       2. *-commutative 38.8%

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

   14. Simplified 38.8%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t\_1 - b \cdot t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -2e-62)
     (- t_1 (* b t_1))
     (if (<= b 1.2e+118)
       (/ x (* b (* a (+ y (/ y b)))))
       (/ x (* y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -2e-62) {
		tmp = t_1 - (b * t_1);
	} else if (b <= 1.2e+118) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-2d-62)) then
        tmp = t_1 - (b * t_1)
    else if (b <= 1.2d+118) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -2e-62) {
		tmp = t_1 - (b * t_1);
	} else if (b <= 1.2e+118) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -2e-62:
		tmp = t_1 - (b * t_1)
	elif b <= 1.2e+118:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -2e-62)
		tmp = Float64(t_1 - Float64(b * t_1));
	elseif (b <= 1.2e+118)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= -2e-62)
		tmp = t_1 - (b * t_1);
	elseif (b <= 1.2e+118)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2e-62], N[(t$95$1 - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+118], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.0000000000000001e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 77.9%

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

      2. exp-neg 77.9%

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

      3. exp-sum 77.9%

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

      4. rem-exp-log 77.9%

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

      5. associate-/l/ 77.9%

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

      6. associate-/r* 77.9%

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

      7. *-commutative 77.9%

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

      8. associate-/r* 77.9%

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

      9. associate-/l* 77.9%

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

      10. *-rgt-identity 77.9%

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

      11. associate-*r* 72.6%

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

      12. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in b around 0 43.9%

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

       1. +-commutative 43.9%

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

       2. mul-1-neg 43.9%

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

       3. unsub-neg 43.9%

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

       4. associate-/r* 45.1%

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

       5. associate-/l* 42.6%

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

       6. associate-/r* 42.7%

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

   11. Simplified 42.7%

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

   if -2.0000000000000001e-62 < b < 1.2e118

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in y around 0 44.3%

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

      1. associate-/l* 47.3%

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

      2. exp-neg 47.4%

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

      3. exp-sum 47.4%

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

      4. rem-exp-log 48.5%

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

      5. associate-/l/ 48.5%

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

      6. associate-/r* 48.5%

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

      7. *-commutative 48.5%

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

      8. associate-/r* 49.1%

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

      9. associate-/l* 49.2%

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

      10. *-rgt-identity 49.2%

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

      11. associate-*r* 49.2%

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

      12. *-commutative 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in b around 0 42.3%

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

       1. distribute-lft-out 44.4%

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

       2. distribute-rgt1-in 44.4%

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

   11. Simplified 44.4%

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

   12. Taylor expanded in b around inf 40.8%

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

       1. associate-/l* 48.3%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 52.5%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 52.5%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 1.2e118 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 100.0%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 100.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 100.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 89.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 89.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 89.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 89.6%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 89.6%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 89.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 89.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 89.6%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 89.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 89.6%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 89.6%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 68.6%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 68.6%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 68.6%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 33.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 33.6%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 33.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 33.6%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 33.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 38.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. *-commutative 38.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot b\right)}} \]

   14. Simplified 38.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} - b \cdot \frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.7% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e-91)
   (- (/ x (* y a)) (/ (* x b) (* y a)))
   (if (<= b 4e+117) (/ x (* b (* a (+ y (/ y b))))) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-91) {
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	} else if (b <= 4e+117) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d-91)) then
        tmp = (x / (y * a)) - ((x * b) / (y * a))
    else if (b <= 4d+117) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-91) {
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	} else if (b <= 4e+117) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e-91:
		tmp = (x / (y * a)) - ((x * b) / (y * a))
	elif b <= 4e+117:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e-91)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x * b) / Float64(y * a)));
	elseif (b <= 4e+117)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e-91)
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	elseif (b <= 4e+117)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e-91], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+117], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.7000000000000002e-91

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 90.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 90.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 90.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 90.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 90.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 73.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 73.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 73.4%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 73.5%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 73.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 73.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 73.5%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 74.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 74.6%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 74.6%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 69.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 69.8%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 44.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   if -3.7000000000000002e-91 < b < 4.0000000000000002e117

   1. Initial program 95.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 77.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 77.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 77.3%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 77.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 77.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 44.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 48.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 48.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 48.2%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 49.3%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 49.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 49.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 49.3%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 49.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 49.4%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 49.4%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 49.4%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 49.4%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 42.1%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 44.3%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 44.3%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 44.3%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 41.2%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 49.2%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 52.9%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 52.9%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 4.0000000000000002e117 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 100.0%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 100.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 100.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 89.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 89.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 89.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 89.6%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 89.6%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 89.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 89.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 89.6%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 89.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 89.6%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 89.6%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 68.6%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 68.6%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 68.6%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 33.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 33.6%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 33.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 33.6%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 33.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 38.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. *-commutative 38.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot b\right)}} \]

   14. Simplified 38.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.9% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.4e-18) (* (/ x (* y a)) (- (- -1.0) b)) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.4e-18) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.4d-18) then
        tmp = (x / (y * a)) * (-(-1.0d0) - b)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.4e-18) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.4e-18:
		tmp = (x / (y * a)) * (-(-1.0) - b)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.4e-18)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(Float64(-(-1.0)) - b));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.4e-18)
		tmp = (x / (y * a)) * (-(-1.0) - b);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.4e-18], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.40000000000000001e-18

   1. Initial program 96.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 82.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 82.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 82.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 82.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 82.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 56.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 58.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 58.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 58.2%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 59.1%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 59.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 59.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 59.1%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 59.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 59.6%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 59.6%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 57.5%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 57.5%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 57.5%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 32.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 34.2%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 34.2%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 34.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around 0 42.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 42.8%

          \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

       2. remove-double-neg 42.8%

          \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. distribute-neg-out 42.8%

          \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       4. associate-/l* 40.2%

          \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} + \left(-\frac{x}{a \cdot y}\right)\right) \]

       5. mul-1-neg 40.2%

          \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} + \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       6. distribute-rgt-out 45.1%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

       7. *-commutative 45.1%

          \[\leadsto -\frac{x}{\color{blue}{y \cdot a}} \cdot \left(b + -1\right) \]

   14. Simplified 45.1%

       \[\leadsto \color{blue}{-\frac{x}{y \cdot a} \cdot \left(b + -1\right)} \]

   if 3.40000000000000001e-18 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 92.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 92.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 92.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 92.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 92.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 75.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 75.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 75.9%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 75.9%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 75.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 75.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 75.9%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 75.9%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 75.9%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 75.9%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 63.5%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 63.5%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 63.5%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 32.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 32.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 32.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 32.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 32.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 35.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. *-commutative 35.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot b\right)}} \]

   14. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.0% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.1e-181) (* (/ x y) (/ 1.0 a)) (/ x (* y (* a (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.1e-181) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.1d-181) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (y * (a * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.1e-181) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.1e-181:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.1e-181)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.1e-181)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.1e-181], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.1000000000000001e-181

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 75.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 75.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 76.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 76.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 76.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y \cdot e^{b}} \]

      2. *-commutative 67.1%

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{\color{blue}{e^{b} \cdot y}} \]

      3. times-frac 66.8%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

      4. exp-to-pow 67.6%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      5. sub-neg 67.6%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      6. metadata-eval 67.6%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \cdot \frac{x}{y} \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 60.3%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right)}} \cdot \frac{x}{y} \]
   9. Step-by-step derivation

      1. exp-to-pow 61.1%

         \[\leadsto \color{blue}{{a}^{\left(t - 1\right)}} \cdot \frac{x}{y} \]

      2. sub-neg 61.1%

         \[\leadsto {a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot \frac{x}{y} \]

      3. metadata-eval 61.1%

         \[\leadsto {a}^{\left(t + \color{blue}{-1}\right)} \cdot \frac{x}{y} \]

   10. Simplified 61.1%

       \[\leadsto \color{blue}{{a}^{\left(t + -1\right)}} \cdot \frac{x}{y} \]

   11. Taylor expanded in t around 0 42.7%

       \[\leadsto \color{blue}{\frac{1}{a}} \cdot \frac{x}{y} \]

   if 4.1000000000000001e-181 < b

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 86.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 86.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 86.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 86.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 86.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 62.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 64.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 64.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 64.3%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 64.7%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 64.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 64.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 64.7%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 64.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 64.8%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 64.8%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 56.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 56.8%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 36.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 36.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 36.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 36.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in x around 0 36.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 36.8%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot \left(1 + b\right)\right) \cdot a}} \]

       2. associate-*l* 38.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(\left(1 + b\right) \cdot a\right)}} \]

   14. Simplified 38.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(\left(1 + b\right) \cdot a\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.2e-256) (/ x (* y a)) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.2e-256) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 2.2d-256) then
        tmp = x / (y * a)
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.2e-256) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.2e-256:
		tmp = x / (y * a)
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.2e-256)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.2e-256)
		tmp = x / (y * a);
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.2e-256], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.2000000000000001e-256

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 85.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 85.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 85.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 85.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 85.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 63.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 64.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 64.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 64.2%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 64.9%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 64.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 64.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 64.9%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 65.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 65.6%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 65.6%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 60.0%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 60.0%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 60.0%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 41.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

   if 2.2000000000000001e-256 < y

   1. Initial program 96.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 82.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. *-commutative 64.3%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y \cdot e^{b}} \]

      2. *-commutative 64.3%

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{\color{blue}{e^{b} \cdot y}} \]

      3. times-frac 66.2%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

      4. exp-to-pow 66.8%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      5. sub-neg 66.8%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      6. metadata-eval 66.8%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \cdot \frac{x}{y} \]

   7. Simplified 66.8%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 52.8%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right)}} \cdot \frac{x}{y} \]
   9. Step-by-step derivation

      1. exp-to-pow 53.3%

         \[\leadsto \color{blue}{{a}^{\left(t - 1\right)}} \cdot \frac{x}{y} \]

      2. sub-neg 53.3%

         \[\leadsto {a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot \frac{x}{y} \]

      3. metadata-eval 53.3%

         \[\leadsto {a}^{\left(t + \color{blue}{-1}\right)} \cdot \frac{x}{y} \]

   10. Simplified 53.3%

       \[\leadsto \color{blue}{{a}^{\left(t + -1\right)}} \cdot \frac{x}{y} \]

   11. Taylor expanded in t around 0 35.7%

       \[\leadsto \color{blue}{\frac{1}{a}} \cdot \frac{x}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6e-35) (* (/ x y) (/ 1.0 a)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-35) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6d-35) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-35) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6e-35:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6e-35)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6e-35)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6e-35], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.99999999999999978e-35

   1. Initial program 96.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y \cdot e^{b}} \]

      2. *-commutative 67.4%

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{\color{blue}{e^{b} \cdot y}} \]

      3. times-frac 66.7%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

      4. exp-to-pow 67.5%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      5. sub-neg 67.5%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      6. metadata-eval 67.5%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \cdot \frac{x}{y} \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 61.2%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right)}} \cdot \frac{x}{y} \]
   9. Step-by-step derivation

      1. exp-to-pow 62.0%

         \[\leadsto \color{blue}{{a}^{\left(t - 1\right)}} \cdot \frac{x}{y} \]

      2. sub-neg 62.0%

         \[\leadsto {a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot \frac{x}{y} \]

      3. metadata-eval 62.0%

         \[\leadsto {a}^{\left(t + \color{blue}{-1}\right)} \cdot \frac{x}{y} \]

   10. Simplified 62.0%

       \[\leadsto \color{blue}{{a}^{\left(t + -1\right)}} \cdot \frac{x}{y} \]

   11. Taylor expanded in t around 0 42.9%

       \[\leadsto \color{blue}{\frac{1}{a}} \cdot \frac{x}{y} \]

   if 5.99999999999999978e-35 < b

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 90.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 90.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 90.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 90.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 90.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 72.0%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 72.0%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 72.0%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 72.0%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 72.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 72.0%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 72.0%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 72.0%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 72.0%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 60.7%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 60.7%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 60.7%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 32.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 32.6%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 32.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 32.6%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 31.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 31.7%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 31.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.0% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4e-106) (* (/ x y) (/ 1.0 a)) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4e-106) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4d-106) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4e-106) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4e-106:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4e-106)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4e-106)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4e-106], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.99999999999999976e-106

   1. Initial program 96.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y \cdot e^{b}} \]

      2. *-commutative 67.3%

         \[\leadsto \frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{\color{blue}{e^{b} \cdot y}} \]

      3. times-frac 67.0%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

      4. exp-to-pow 67.8%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      5. sub-neg 67.8%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      6. metadata-eval 67.8%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \cdot \frac{x}{y} \]

   7. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}} \]

   8. Taylor expanded in b around 0 61.0%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right)}} \cdot \frac{x}{y} \]
   9. Step-by-step derivation

      1. exp-to-pow 61.8%

         \[\leadsto \color{blue}{{a}^{\left(t - 1\right)}} \cdot \frac{x}{y} \]

      2. sub-neg 61.8%

         \[\leadsto {a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot \frac{x}{y} \]

      3. metadata-eval 61.8%

         \[\leadsto {a}^{\left(t + \color{blue}{-1}\right)} \cdot \frac{x}{y} \]

   10. Simplified 61.8%

       \[\leadsto \color{blue}{{a}^{\left(t + -1\right)}} \cdot \frac{x}{y} \]

   11. Taylor expanded in t around 0 42.6%

       \[\leadsto \color{blue}{\frac{1}{a}} \cdot \frac{x}{y} \]

   if 3.99999999999999976e-106 < b

   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 t around 0 89.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 89.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 89.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 89.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 89.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 66.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 67.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

      2. exp-neg 67.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      3. exp-sum 67.2%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      4. rem-exp-log 67.3%

         \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      5. associate-/l/ 67.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

      6. associate-/r* 67.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

      7. *-commutative 67.3%

         \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

      8. associate-/r* 67.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      9. associate-/l* 67.3%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

      10. *-rgt-identity 67.3%

          \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      11. associate-*r* 58.1%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      12. *-commutative 58.1%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   8. Simplified 58.1%

      \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

   9. Taylor expanded in b around 0 35.1%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 35.1%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. distribute-rgt1-in 35.1%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 35.1%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 33.3%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 36.7%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. *-commutative 36.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot b\right)}} \]

   14. Simplified 36.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.1% 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 97.5%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 85.0%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
4. Step-by-step derivation

   1. +-commutative 85.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

   2. mul-1-neg 85.0%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   3. unsub-neg 85.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

5. Simplified 85.0%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

6. Taylor expanded in y around 0 61.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
7. Step-by-step derivation

   1. associate-/l* 62.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{-\left(b + \log a\right)}}{y}} \]

   2. exp-neg 62.7%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

   3. exp-sum 62.7%

      \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

   4. rem-exp-log 63.3%

      \[\leadsto x \cdot \frac{\frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

   5. associate-/l/ 63.3%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   6. associate-/r* 63.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b} \cdot y}} \]

   7. *-commutative 63.3%

      \[\leadsto x \cdot \frac{\frac{1}{a}}{\color{blue}{y \cdot e^{b}}} \]

   8. associate-/r* 63.7%

      \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. associate-/l* 63.7%

      \[\leadsto \color{blue}{\frac{x \cdot 1}{a \cdot \left(y \cdot e^{b}\right)}} \]

   10. *-rgt-identity 63.7%

       \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   11. associate-*r* 59.0%

       \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   12. *-commutative 59.0%

       \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

8. Simplified 59.0%

   \[\leadsto \color{blue}{\frac{x}{\left(y \cdot a\right) \cdot e^{b}}} \]

9. Taylor expanded in b around 0 35.4%

   \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

10. Final simplification 35.4%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 73.6% 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 2024071 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))