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

Percentage Accurate: 98.3% → 98.3%

Time: 22.8s

Alternatives: 23

Speedup: 1.0×

• 46.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+34} \lor \neg \left(y \leq 3.8 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+34) (not (<= y 3.8e-32)))
   (/ (* 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 <= -6.2e+34) || !(y <= 3.8e-32)) {
		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 <= (-6.2d+34)) .or. (.not. (y <= 3.8d-32))) 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 <= -6.2e+34) || !(y <= 3.8e-32)) {
		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 <= -6.2e+34) or not (y <= 3.8e-32):
		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 <= -6.2e+34) || !(y <= 3.8e-32))
		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 <= -6.2e+34) || ~((y <= 3.8e-32)))
		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, -6.2e+34], N[Not[LessEqual[y, 3.8e-32]], $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 < -6.19999999999999955e34 or 3.80000000000000008e-32 < y

   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 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   5. Simplified 93.8%

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

   if -6.19999999999999955e34 < y < 3.80000000000000008e-32

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 96.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+34} \lor \neg \left(y \leq 3.8 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+36} \lor \neg \left(y \leq 1.02\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.5e+36) (not (<= y 1.02)))
   (* 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 <= -7.5e+36) || !(y <= 1.02)) {
		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 <= (-7.5d+36)) .or. (.not. (y <= 1.02d0))) 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 <= -7.5e+36) || !(y <= 1.02)) {
		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 <= -7.5e+36) or not (y <= 1.02):
		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 <= -7.5e+36) || !(y <= 1.02))
		tmp = Float64(x * Float64(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 <= -7.5e+36) || ~((y <= 1.02)))
		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, -7.5e+36], N[Not[LessEqual[y, 1.02]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $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 < -7.50000000000000054e36 or 1.02 < y

   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 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in b around 0 87.9%

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

      1. associate-/l* 87.9%

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

      2. div-exp 87.9%

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

      3. *-commutative 87.9%

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

      4. exp-to-pow 87.9%

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

      5. rem-exp-log 88.0%

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

   8. Simplified 88.0%

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

   if -7.50000000000000054e36 < y < 1.02

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 96.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+36} \lor \neg \left(y \leq 1.02\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+33} \lor \neg \left(y \leq 1.02\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.12e+33) (not (<= y 1.02)))
   (* 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 <= -1.12e+33) || !(y <= 1.02)) {
		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 <= (-1.12d+33)) .or. (.not. (y <= 1.02d0))) 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 <= -1.12e+33) || !(y <= 1.02)) {
		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 <= -1.12e+33) or not (y <= 1.02):
		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 <= -1.12e+33) || !(y <= 1.02))
		tmp = Float64(x * Float64(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 <= -1.12e+33) || ~((y <= 1.02)))
		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, -1.12e+33], N[Not[LessEqual[y, 1.02]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $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 < -1.12e33 or 1.02 < y

   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 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in b around 0 87.9%

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

      1. associate-/l* 87.9%

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

      2. div-exp 87.9%

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

      3. *-commutative 87.9%

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

      4. exp-to-pow 87.9%

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

      5. rem-exp-log 88.0%

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

   8. Simplified 88.0%

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

   if -1.12e33 < y < 1.02

   1. Initial program 96.8%

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

      1. associate-/l* 96.3%

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

      2. associate--l+ 96.3%

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

      3. exp-sum 95.6%

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

      4. associate-/l* 95.6%

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

      5. *-commutative 95.6%

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

      6. exp-to-pow 95.6%

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

      7. exp-diff 87.3%

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

      8. *-commutative 87.3%

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

      9. exp-to-pow 88.1%

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

      10. sub-neg 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 85.5%

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

      1. exp-to-pow 86.4%

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

      2. sub-neg 86.4%

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

      3. metadata-eval 86.4%

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

      4. associate-*r/ 88.9%

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

   7. Simplified 88.9%

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

      1. unpow-prod-up 88.9%

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

      2. unpow-1 88.9%

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

   9. Applied egg-rr 88.9%

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

       1. associate-*r/ 88.9%

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

       2. *-rgt-identity 88.9%

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

   11. Simplified 88.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+33} \lor \neg \left(y \leq 1.02\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{\frac{x}{y}}{e^{b}}}{a}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.02:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -5.5e+33)
     t_1
     (if (<= y -3e-88)
       (/ (/ (/ x y) (exp b)) a)
       (if (<= y 4.4e-122)
         (* x (/ (/ (pow a t) a) y))
         (if (<= y 1.02) (/ x (* a (* y (exp b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(z, y) / a) / y);
	double tmp;
	if (y <= -5.5e+33) {
		tmp = t_1;
	} else if (y <= -3e-88) {
		tmp = ((x / y) / exp(b)) / a;
	} else if (y <= 4.4e-122) {
		tmp = x * ((pow(a, t) / a) / y);
	} else if (y <= 1.02) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (((z ** y) / a) / y)
    if (y <= (-5.5d+33)) then
        tmp = t_1
    else if (y <= (-3d-88)) then
        tmp = ((x / y) / exp(b)) / a
    else if (y <= 4.4d-122) then
        tmp = x * (((a ** t) / a) / y)
    else if (y <= 1.02d0) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((Math.pow(z, y) / a) / y);
	double tmp;
	if (y <= -5.5e+33) {
		tmp = t_1;
	} else if (y <= -3e-88) {
		tmp = ((x / y) / Math.exp(b)) / a;
	} else if (y <= 4.4e-122) {
		tmp = x * ((Math.pow(a, t) / a) / y);
	} else if (y <= 1.02) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(z, y) / a) / y)
	tmp = 0
	if y <= -5.5e+33:
		tmp = t_1
	elif y <= -3e-88:
		tmp = ((x / y) / math.exp(b)) / a
	elif y <= 4.4e-122:
		tmp = x * ((math.pow(a, t) / a) / y)
	elif y <= 1.02:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -5.5e+33)
		tmp = t_1;
	elseif (y <= -3e-88)
		tmp = Float64(Float64(Float64(x / y) / exp(b)) / a);
	elseif (y <= 4.4e-122)
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / y));
	elseif (y <= 1.02)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((z ^ y) / a) / y);
	tmp = 0.0;
	if (y <= -5.5e+33)
		tmp = t_1;
	elseif (y <= -3e-88)
		tmp = ((x / y) / exp(b)) / a;
	elseif (y <= 4.4e-122)
		tmp = x * (((a ^ t) / a) / y);
	elseif (y <= 1.02)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+33], t$95$1, If[LessEqual[y, -3e-88], N[(N[(N[(x / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 4.4e-122], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5000000000000006e33 or 1.02 < y

   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 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in b around 0 87.9%

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

      1. associate-/l* 87.9%

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

      2. div-exp 87.9%

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

      3. *-commutative 87.9%

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

      4. exp-to-pow 87.9%

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

      5. rem-exp-log 88.0%

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

   8. Simplified 88.0%

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

   if -5.5000000000000006e33 < y < -2.9999999999999999e-88

   1. Initial program 98.7%

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

      1. associate-/l* 95.1%

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

      2. associate--l+ 95.1%

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

      3. exp-sum 90.5%

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

      4. associate-/l* 90.5%

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

      5. *-commutative 90.5%

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

      6. exp-to-pow 90.5%

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

      7. exp-diff 81.4%

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

      8. *-commutative 81.4%

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

      9. exp-to-pow 82.1%

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

      10. sub-neg 82.1%

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

      11. metadata-eval 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in y around 0 80.5%

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

      1. exp-to-pow 81.7%

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

      2. sub-neg 81.7%

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

      3. metadata-eval 81.7%

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

      4. associate-*r/ 86.7%

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

   7. Simplified 86.7%

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

      1. unpow-prod-up 86.7%

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

      2. unpow-1 86.7%

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

   9. Applied egg-rr 86.7%

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

       1. associate-*r/ 86.7%

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

       2. *-rgt-identity 86.7%

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

   11. Simplified 86.7%

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

   12. Taylor expanded in t around 0 78.2%

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

       1. *-lft-identity 78.2%

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

       2. times-frac 86.7%

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

       3. associate-*l/ 86.7%

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

       4. *-lft-identity 86.7%

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

       5. associate-/r* 86.7%

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

   14. Simplified 86.7%

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

   if -2.9999999999999999e-88 < y < 4.4e-122

   1. Initial program 95.8%

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

      1. associate-/l* 95.9%

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

      2. associate--l+ 95.9%

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

      3. exp-sum 95.9%

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

      4. associate-/l* 95.9%

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

      5. *-commutative 95.9%

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

      6. exp-to-pow 95.9%

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

      7. exp-diff 91.3%

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

      8. *-commutative 91.3%

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

      9. exp-to-pow 92.2%

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

      10. sub-neg 92.2%

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

      11. metadata-eval 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 88.9%

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

      1. exp-to-pow 89.7%

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

      2. sub-neg 89.7%

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

      3. metadata-eval 89.7%

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

      4. associate-*r/ 92.2%

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

   7. Simplified 92.2%

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

      1. unpow-prod-up 92.2%

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

      2. unpow-1 92.2%

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

   9. Applied egg-rr 92.2%

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

       1. associate-*r/ 92.2%

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

       2. *-rgt-identity 92.2%

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

   11. Simplified 92.2%

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

   12. Taylor expanded in b around 0 76.9%

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

   if 4.4e-122 < y < 1.02

   1. Initial program 98.9%

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

      1. associate-/l* 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 98.9%

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

      4. associate-/l* 98.9%

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

      5. *-commutative 98.9%

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

      6. exp-to-pow 98.9%

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

      7. exp-diff 78.1%

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

      8. *-commutative 78.1%

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

      9. exp-to-pow 78.7%

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

      10. sub-neg 78.7%

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

      11. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. exp-to-pow 78.7%

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

      2. sub-neg 78.7%

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

      3. metadata-eval 78.7%

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

      4. associate-*r/ 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around 0 89.6%

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

Alternative 6: 61.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -0.0031:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -0.0031)
     t_2
     (if (<= b -8.5e-289)
       t_1
       (if (<= b 1.65e-201) (/ (/ x a) y) (if (<= b 5e-34) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double t_2 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -0.0031) {
		tmp = t_2;
	} else if (b <= -8.5e-289) {
		tmp = t_1;
	} else if (b <= 1.65e-201) {
		tmp = (x / a) / y;
	} else if (b <= 5e-34) {
		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 / (b * (a * (y + (y / b))))
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-0.0031d0)) then
        tmp = t_2
    else if (b <= (-8.5d-289)) then
        tmp = t_1
    else if (b <= 1.65d-201) then
        tmp = (x / a) / y
    else if (b <= 5d-34) 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 / (b * (a * (y + (y / b))));
	double t_2 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -0.0031) {
		tmp = t_2;
	} else if (b <= -8.5e-289) {
		tmp = t_1;
	} else if (b <= 1.65e-201) {
		tmp = (x / a) / y;
	} else if (b <= 5e-34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	t_2 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -0.0031:
		tmp = t_2
	elif b <= -8.5e-289:
		tmp = t_1
	elif b <= 1.65e-201:
		tmp = (x / a) / y
	elif b <= 5e-34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -0.0031)
		tmp = t_2;
	elseif (b <= -8.5e-289)
		tmp = t_1;
	elseif (b <= 1.65e-201)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 5e-34)
		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 / (b * (a * (y + (y / b))));
	t_2 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -0.0031)
		tmp = t_2;
	elseif (b <= -8.5e-289)
		tmp = t_1;
	elseif (b <= 1.65e-201)
		tmp = (x / a) / y;
	elseif (b <= 5e-34)
		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[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.0031], t$95$2, If[LessEqual[b, -8.5e-289], t$95$1, If[LessEqual[b, 1.65e-201], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5e-34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.00309999999999999989 or 5.0000000000000003e-34 < b

   1. Initial program 99.9%

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

      1. associate-/l* 99.2%

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

      2. associate--l+ 99.2%

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

      3. exp-sum 78.3%

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

      4. associate-/l* 78.3%

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

      5. *-commutative 78.3%

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

      6. exp-to-pow 78.3%

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

      7. exp-diff 65.7%

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

      8. *-commutative 65.7%

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

      9. exp-to-pow 65.7%

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

      10. sub-neg 65.7%

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

      11. metadata-eval 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. exp-to-pow 70.3%

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

      2. sub-neg 70.3%

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

      3. metadata-eval 70.3%

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

      4. associate-*r/ 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in t around 0 80.3%

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

   if -0.00309999999999999989 < b < -8.49999999999999931e-289 or 1.6500000000000002e-201 < b < 5.0000000000000003e-34

   1. Initial program 96.2%

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

      1. associate-/l* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 91.4%

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

      4. associate-/l* 89.2%

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

      5. *-commutative 89.2%

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

      6. exp-to-pow 89.2%

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

      7. exp-diff 89.2%

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

      8. *-commutative 89.2%

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

      9. exp-to-pow 89.9%

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

      10. sub-neg 89.9%

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

      11. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. exp-to-pow 63.8%

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

      2. sub-neg 63.8%

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

      3. metadata-eval 63.8%

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

      4. associate-*r/ 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in t around 0 33.2%

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

   9. Taylor expanded in b around 0 31.9%

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

       1. distribute-lft-out 33.2%

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

       2. *-commutative 33.2%

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

   11. Simplified 33.2%

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

   12. Taylor expanded in b around inf 29.4%

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

       1. associate-/l* 41.5%

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

       2. distribute-lft-out 47.2%

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

   14. Simplified 47.2%

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

   if -8.49999999999999931e-289 < b < 1.6500000000000002e-201

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. exp-to-pow 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in t around 0 49.7%

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

Alternative 7: 75.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -52000000 \lor \neg \left(b \leq 112\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -52000000.0) (not (<= b 112.0)))
   (/ x (* a (* y (exp b))))
   (* x (/ (/ (pow a t) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -52000000.0) || !(b <= 112.0)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * ((pow(a, t) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-52000000.0d0)) .or. (.not. (b <= 112.0d0))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (((a ** t) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -52000000.0) || !(b <= 112.0)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * ((Math.pow(a, t) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -52000000.0) or not (b <= 112.0):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * ((math.pow(a, t) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -52000000.0) || !(b <= 112.0))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -52000000.0) || ~((b <= 112.0)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (((a ^ t) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -52000000.0], N[Not[LessEqual[b, 112.0]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2e7 or 112 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 79.5%

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

      4. associate-/l* 79.5%

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

      5. *-commutative 79.5%

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

      6. exp-to-pow 79.5%

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

      7. exp-diff 66.4%

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

      8. *-commutative 66.4%

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

      9. exp-to-pow 66.4%

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

      10. sub-neg 66.4%

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

      11. metadata-eval 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. exp-to-pow 69.0%

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

      2. sub-neg 69.0%

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

      3. metadata-eval 69.0%

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

      4. associate-*r/ 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in t around 0 85.5%

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

   if -5.2e7 < b < 112

   1. Initial program 96.7%

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

      1. associate-/l* 96.2%

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

      2. associate--l+ 96.2%

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

      3. exp-sum 88.8%

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

      4. associate-/l* 85.8%

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

      5. *-commutative 85.8%

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

      6. exp-to-pow 85.8%

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

      7. exp-diff 85.1%

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

      8. *-commutative 85.1%

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

      9. exp-to-pow 86.0%

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

      10. sub-neg 86.0%

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

      11. metadata-eval 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. exp-to-pow 68.8%

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

      2. sub-neg 68.8%

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

      3. metadata-eval 68.8%

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

      4. associate-*r/ 66.9%

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

   7. Simplified 66.9%

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

      1. unpow-prod-up 66.9%

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

      2. unpow-1 66.9%

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

   9. Applied egg-rr 66.9%

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

       1. associate-*r/ 66.9%

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

       2. *-rgt-identity 66.9%

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

   11. Simplified 66.9%

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

   12. Taylor expanded in b around 0 67.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -52000000 \lor \neg \left(b \leq 112\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ t_2 := \frac{x}{y} \cdot 0.5 - \frac{x}{y}\\ \mathbf{if}\;b \leq -0.0058:\\ \;\;\;\;\frac{\frac{x}{y} - b \cdot \left(\frac{x}{y} + b \cdot \left(t\_2 - b \cdot \left(t\_2 - \left(\frac{x}{y} \cdot -0.5 + \frac{x}{y} \cdot 0.16666666666666666\right)\right)\right)\right)}{a}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b))))))
        (t_2 (- (* (/ x y) 0.5) (/ x y))))
   (if (<= b -0.0058)
     (/
      (-
       (/ x y)
       (*
        b
        (+
         (/ x y)
         (*
          b
          (-
           t_2
           (*
            b
            (- t_2 (+ (* (/ x y) -0.5) (* (/ x y) 0.16666666666666666)))))))))
      a)
     (if (<= b -2.4e-281)
       t_1
       (if (<= b 1.8e-201)
         (/ (/ x a) y)
         (if (<= b 2e-56)
           t_1
           (/
            x
            (*
             a
             (+
              y
              (*
               b
               (+ y (* b (* y (+ 0.5 (* b 0.16666666666666666)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double t_2 = ((x / y) * 0.5) - (x / y);
	double tmp;
	if (b <= -0.0058) {
		tmp = ((x / y) - (b * ((x / y) + (b * (t_2 - (b * (t_2 - (((x / y) * -0.5) + ((x / y) * 0.16666666666666666))))))))) / a;
	} else if (b <= -2.4e-281) {
		tmp = t_1;
	} else if (b <= 1.8e-201) {
		tmp = (x / a) / y;
	} else if (b <= 2e-56) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 / (b * (a * (y + (y / b))))
    t_2 = ((x / y) * 0.5d0) - (x / y)
    if (b <= (-0.0058d0)) then
        tmp = ((x / y) - (b * ((x / y) + (b * (t_2 - (b * (t_2 - (((x / y) * (-0.5d0)) + ((x / y) * 0.16666666666666666d0))))))))) / a
    else if (b <= (-2.4d-281)) then
        tmp = t_1
    else if (b <= 1.8d-201) then
        tmp = (x / a) / y
    else if (b <= 2d-56) then
        tmp = t_1
    else
        tmp = x / (a * (y + (b * (y + (b * (y * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 / (b * (a * (y + (y / b))));
	double t_2 = ((x / y) * 0.5) - (x / y);
	double tmp;
	if (b <= -0.0058) {
		tmp = ((x / y) - (b * ((x / y) + (b * (t_2 - (b * (t_2 - (((x / y) * -0.5) + ((x / y) * 0.16666666666666666))))))))) / a;
	} else if (b <= -2.4e-281) {
		tmp = t_1;
	} else if (b <= 1.8e-201) {
		tmp = (x / a) / y;
	} else if (b <= 2e-56) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	t_2 = ((x / y) * 0.5) - (x / y)
	tmp = 0
	if b <= -0.0058:
		tmp = ((x / y) - (b * ((x / y) + (b * (t_2 - (b * (t_2 - (((x / y) * -0.5) + ((x / y) * 0.16666666666666666))))))))) / a
	elif b <= -2.4e-281:
		tmp = t_1
	elif b <= 1.8e-201:
		tmp = (x / a) / y
	elif b <= 2e-56:
		tmp = t_1
	else:
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	t_2 = Float64(Float64(Float64(x / y) * 0.5) - Float64(x / y))
	tmp = 0.0
	if (b <= -0.0058)
		tmp = Float64(Float64(Float64(x / y) - Float64(b * Float64(Float64(x / y) + Float64(b * Float64(t_2 - Float64(b * Float64(t_2 - Float64(Float64(Float64(x / y) * -0.5) + Float64(Float64(x / y) * 0.16666666666666666))))))))) / a);
	elseif (b <= -2.4e-281)
		tmp = t_1;
	elseif (b <= 1.8e-201)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 2e-56)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(y * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	t_2 = ((x / y) * 0.5) - (x / y);
	tmp = 0.0;
	if (b <= -0.0058)
		tmp = ((x / y) - (b * ((x / y) + (b * (t_2 - (b * (t_2 - (((x / y) * -0.5) + ((x / y) * 0.16666666666666666))))))))) / a;
	elseif (b <= -2.4e-281)
		tmp = t_1;
	elseif (b <= 1.8e-201)
		tmp = (x / a) / y;
	elseif (b <= 2e-56)
		tmp = t_1;
	else
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x / y), $MachinePrecision] * 0.5), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.0058], N[(N[(N[(x / y), $MachinePrecision] - N[(b * N[(N[(x / y), $MachinePrecision] + N[(b * N[(t$95$2 - N[(b * N[(t$95$2 - N[(N[(N[(x / y), $MachinePrecision] * -0.5), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.4e-281], t$95$1, If[LessEqual[b, 1.8e-201], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2e-56], t$95$1, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(y * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.0058

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

      3. exp-sum 84.3%

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

      4. associate-/l* 84.3%

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

      5. *-commutative 84.3%

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

      6. exp-to-pow 84.3%

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

      7. exp-diff 68.7%

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

      8. *-commutative 68.7%

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

      9. exp-to-pow 68.7%

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

      10. sub-neg 68.7%

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

      11. metadata-eval 68.7%

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

   3. Simplified 68.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   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. exp-to-pow 73.5%

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

      2. sub-neg 73.5%

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

      3. metadata-eval 73.5%

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

      4. associate-*r/ 78.2%

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

   7. Simplified 78.2%

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

      1. unpow-prod-up 78.2%

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

      2. unpow-1 78.2%

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

   9. Applied egg-rr 78.2%

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

       1. associate-*r/ 78.2%

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

       2. *-rgt-identity 78.2%

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

   11. Simplified 78.2%

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

   12. Taylor expanded in t around 0 89.2%

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

       1. *-lft-identity 89.2%

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

       2. times-frac 89.2%

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

       3. associate-*l/ 89.2%

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

       4. *-lft-identity 89.2%

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

       5. associate-/r* 79.8%

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

   14. Simplified 79.8%

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

   15. Taylor expanded in b around 0 57.9%

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

   if -0.0058 < b < -2.4e-281 or 1.80000000000000016e-201 < b < 2.0000000000000001e-56

   1. Initial program 96.0%

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

      1. associate-/l* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 91.0%

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

      4. associate-/l* 88.6%

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

      5. *-commutative 88.6%

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

      6. exp-to-pow 88.6%

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

      7. exp-diff 88.6%

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

      8. *-commutative 88.6%

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

      9. exp-to-pow 89.4%

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

      10. sub-neg 89.4%

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

      11. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. exp-to-pow 62.1%

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

      2. sub-neg 62.1%

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

      3. metadata-eval 62.1%

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

      4. associate-*r/ 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 32.3%

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

   9. Taylor expanded in b around 0 31.0%

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

       1. distribute-lft-out 32.3%

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

       2. *-commutative 32.3%

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

   11. Simplified 32.3%

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

   12. Taylor expanded in b around inf 28.4%

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

       1. associate-/l* 41.0%

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

       2. distribute-lft-out 47.0%

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

   14. Simplified 47.0%

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

   if -2.4e-281 < b < 1.80000000000000016e-201

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. exp-to-pow 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in t around 0 49.7%

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

   if 2.0000000000000001e-56 < b

   1. Initial program 99.9%

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

      1. associate-/l* 98.7%

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

      2. associate--l+ 98.7%

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

      3. exp-sum 74.4%

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

      4. associate-/l* 74.4%

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

      5. *-commutative 74.4%

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

      6. exp-to-pow 74.4%

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

      7. exp-diff 64.9%

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

      8. *-commutative 64.9%

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

      9. exp-to-pow 64.9%

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

      10. sub-neg 64.9%

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

      11. metadata-eval 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. exp-to-pow 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-*r/ 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in t around 0 71.0%

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

   9. Taylor expanded in b around 0 58.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot y\right) + 0.5 \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 58.0%

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

       2. distribute-rgt-out 58.0%

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

   11. Simplified 58.0%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0058:\\ \;\;\;\;\frac{\frac{x}{y} - b \cdot \left(\frac{x}{y} + b \cdot \left(\left(\frac{x}{y} \cdot 0.5 - \frac{x}{y}\right) - b \cdot \left(\left(\frac{x}{y} \cdot 0.5 - \frac{x}{y}\right) - \left(\frac{x}{y} \cdot -0.5 + \frac{x}{y} \cdot 0.16666666666666666\right)\right)\right)\right)}{a}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-281}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.6% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -1.55e-16)
     (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
     (if (<= b -3.6e-289)
       t_1
       (if (<= b 1.5e-202)
         (/ (/ x a) y)
         (if (<= b 1.6e-54)
           t_1
           (/
            x
            (*
             a
             (+
              y
              (*
               b
               (+ y (* b (* y (+ 0.5 (* b 0.16666666666666666)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.55e-16) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= -3.6e-289) {
		tmp = t_1;
	} else if (b <= 1.5e-202) {
		tmp = (x / a) / y;
	} else if (b <= 1.6e-54) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 / (b * (a * (y + (y / b))))
    if (b <= (-1.55d-16)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= (-3.6d-289)) then
        tmp = t_1
    else if (b <= 1.5d-202) then
        tmp = (x / a) / y
    else if (b <= 1.6d-54) then
        tmp = t_1
    else
        tmp = x / (a * (y + (b * (y + (b * (y * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.55e-16) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= -3.6e-289) {
		tmp = t_1;
	} else if (b <= 1.5e-202) {
		tmp = (x / a) / y;
	} else if (b <= 1.6e-54) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -1.55e-16:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= -3.6e-289:
		tmp = t_1
	elif b <= 1.5e-202:
		tmp = (x / a) / y
	elif b <= 1.6e-54:
		tmp = t_1
	else:
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -1.55e-16)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= -3.6e-289)
		tmp = t_1;
	elseif (b <= 1.5e-202)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 1.6e-54)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(y * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -1.55e-16)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= -3.6e-289)
		tmp = t_1;
	elseif (b <= 1.5e-202)
		tmp = (x / a) / y;
	elseif (b <= 1.6e-54)
		tmp = t_1;
	else
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e-16], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.6e-289], t$95$1, If[LessEqual[b, 1.5e-202], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.6e-54], t$95$1, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(y * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55e-16

   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 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. distribute-neg-in 86.7%

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

      3. neg-mul-1 86.7%

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

      4. sub-neg 86.7%

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

      5. exp-diff 86.7%

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

      6. neg-mul-1 86.7%

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

      7. log-rec 86.7%

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

      8. rem-exp-log 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in b around 0 41.0%

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

   10. Taylor expanded in x around 0 53.8%

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

   if -1.55e-16 < b < -3.6e-289 or 1.50000000000000005e-202 < b < 1.59999999999999999e-54

   1. Initial program 95.9%

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

      1. associate-/l* 98.1%

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

      2. associate--l+ 98.1%

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

      3. exp-sum 90.7%

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

      4. associate-/l* 88.2%

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

      5. *-commutative 88.2%

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

      6. exp-to-pow 88.2%

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

      7. exp-diff 88.2%

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

      8. *-commutative 88.2%

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

      9. exp-to-pow 89.0%

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

      10. sub-neg 89.0%

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

      11. metadata-eval 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around 0 62.5%

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

      1. exp-to-pow 63.1%

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

      2. sub-neg 63.1%

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

      3. metadata-eval 63.1%

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

      4. associate-*r/ 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in t around 0 33.3%

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

   9. Taylor expanded in b around 0 31.9%

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

       1. distribute-lft-out 33.3%

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

       2. *-commutative 33.3%

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

   11. Simplified 33.3%

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

   12. Taylor expanded in b around inf 29.2%

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

       1. associate-/l* 42.3%

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

       2. distribute-lft-out 48.5%

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

   14. Simplified 48.5%

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

   if -3.6e-289 < b < 1.50000000000000005e-202

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. exp-to-pow 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in t around 0 49.7%

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

   if 1.59999999999999999e-54 < b

   1. Initial program 99.9%

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

      1. associate-/l* 98.7%

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

      2. associate--l+ 98.7%

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

      3. exp-sum 74.4%

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

      4. associate-/l* 74.4%

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

      5. *-commutative 74.4%

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

      6. exp-to-pow 74.4%

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

      7. exp-diff 64.9%

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

      8. *-commutative 64.9%

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

      9. exp-to-pow 64.9%

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

      10. sub-neg 64.9%

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

      11. metadata-eval 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. exp-to-pow 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-*r/ 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in t around 0 71.0%

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

   9. Taylor expanded in b around 0 58.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot y\right) + 0.5 \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 58.0%

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

       2. distribute-rgt-out 58.0%

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

   11. Simplified 58.0%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x + x \cdot \left(b \cdot -0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -7e-18)
     (/ (- (/ x a) (* b (/ (+ x (* x (* b -0.5))) a))) y)
     (if (<= b -1.05e-282)
       t_1
       (if (<= b 1.45e-201)
         (/ (/ x a) y)
         (if (<= b 2e-56)
           t_1
           (/
            x
            (*
             a
             (+
              y
              (*
               b
               (+ y (* b (* y (+ 0.5 (* b 0.16666666666666666)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -7e-18) {
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y;
	} else if (b <= -1.05e-282) {
		tmp = t_1;
	} else if (b <= 1.45e-201) {
		tmp = (x / a) / y;
	} else if (b <= 2e-56) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 / (b * (a * (y + (y / b))))
    if (b <= (-7d-18)) then
        tmp = ((x / a) - (b * ((x + (x * (b * (-0.5d0)))) / a))) / y
    else if (b <= (-1.05d-282)) then
        tmp = t_1
    else if (b <= 1.45d-201) then
        tmp = (x / a) / y
    else if (b <= 2d-56) then
        tmp = t_1
    else
        tmp = x / (a * (y + (b * (y + (b * (y * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -7e-18) {
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y;
	} else if (b <= -1.05e-282) {
		tmp = t_1;
	} else if (b <= 1.45e-201) {
		tmp = (x / a) / y;
	} else if (b <= 2e-56) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -7e-18:
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y
	elif b <= -1.05e-282:
		tmp = t_1
	elif b <= 1.45e-201:
		tmp = (x / a) / y
	elif b <= 2e-56:
		tmp = t_1
	else:
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -7e-18)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x + Float64(x * Float64(b * -0.5))) / a))) / y);
	elseif (b <= -1.05e-282)
		tmp = t_1;
	elseif (b <= 1.45e-201)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 2e-56)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(y * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -7e-18)
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y;
	elseif (b <= -1.05e-282)
		tmp = t_1;
	elseif (b <= 1.45e-201)
		tmp = (x / a) / y;
	elseif (b <= 2e-56)
		tmp = t_1;
	else
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e-18], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x + N[(x * N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.05e-282], t$95$1, If[LessEqual[b, 1.45e-201], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2e-56], t$95$1, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(y * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.9999999999999997e-18

   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 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. distribute-neg-in 86.7%

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

      3. neg-mul-1 86.7%

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

      4. sub-neg 86.7%

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

      5. exp-diff 86.7%

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

      6. neg-mul-1 86.7%

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

      7. log-rec 86.7%

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

      8. rem-exp-log 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in b around 0 41.0%

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

   10. Taylor expanded in b around 0 41.0%

       \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) + -1 \cdot \frac{x}{a}\right)} + \frac{x}{a}}{y} \]
   11. Step-by-step derivation

       1. neg-mul-1 41.0%

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

       2. sub-neg 41.0%

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

       3. distribute-rgt-out 48.4%

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

       4. metadata-eval 48.4%

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

       5. associate-*l/ 48.4%

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

       6. metadata-eval 48.4%

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

       7. distribute-rgt-out 48.4%

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

       8. associate-/l* 49.6%

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

       9. associate-*r/ 49.6%

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

       10. div-sub 49.6%

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

   12. Simplified 49.6%

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

   if -6.9999999999999997e-18 < b < -1.05000000000000006e-282 or 1.4500000000000001e-201 < b < 2.0000000000000001e-56

   1. Initial program 95.9%

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

      1. associate-/l* 98.1%

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

      2. associate--l+ 98.1%

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

      3. exp-sum 90.7%

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

      4. associate-/l* 88.2%

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

      5. *-commutative 88.2%

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

      6. exp-to-pow 88.2%

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

      7. exp-diff 88.2%

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

      8. *-commutative 88.2%

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

      9. exp-to-pow 89.0%

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

      10. sub-neg 89.0%

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

      11. metadata-eval 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around 0 62.5%

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

      1. exp-to-pow 63.1%

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

      2. sub-neg 63.1%

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

      3. metadata-eval 63.1%

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

      4. associate-*r/ 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in t around 0 33.3%

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

   9. Taylor expanded in b around 0 31.9%

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

       1. distribute-lft-out 33.3%

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

       2. *-commutative 33.3%

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

   11. Simplified 33.3%

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

   12. Taylor expanded in b around inf 29.2%

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

       1. associate-/l* 42.3%

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

       2. distribute-lft-out 48.5%

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

   14. Simplified 48.5%

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

   if -1.05000000000000006e-282 < b < 1.4500000000000001e-201

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. exp-to-pow 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in t around 0 49.7%

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

   if 2.0000000000000001e-56 < b

   1. Initial program 99.9%

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

      1. associate-/l* 98.7%

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

      2. associate--l+ 98.7%

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

      3. exp-sum 74.4%

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

      4. associate-/l* 74.4%

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

      5. *-commutative 74.4%

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

      6. exp-to-pow 74.4%

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

      7. exp-diff 64.9%

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

      8. *-commutative 64.9%

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

      9. exp-to-pow 64.9%

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

      10. sub-neg 64.9%

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

      11. metadata-eval 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. exp-to-pow 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-*r/ 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in t around 0 71.0%

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

   9. Taylor expanded in b around 0 58.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot y\right) + 0.5 \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 58.0%

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

       2. distribute-rgt-out 58.0%

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

   11. Simplified 58.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x + x \cdot \left(b \cdot -0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x + x \cdot \left(b \cdot -0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -3.4e-17)
     (/ (- (/ x a) (* b (/ (+ x (* x (* b -0.5))) a))) y)
     (if (<= b -3.3e-288)
       t_1
       (if (<= b 5.5e-203)
         (/ (/ x a) y)
         (if (<= b 4e-32)
           t_1
           (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -3.4e-17) {
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y;
	} else if (b <= -3.3e-288) {
		tmp = t_1;
	} else if (b <= 5.5e-203) {
		tmp = (x / a) / y;
	} else if (b <= 4e-32) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 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 / (b * (a * (y + (y / b))))
    if (b <= (-3.4d-17)) then
        tmp = ((x / a) - (b * ((x + (x * (b * (-0.5d0)))) / a))) / y
    else if (b <= (-3.3d-288)) then
        tmp = t_1
    else if (b <= 5.5d-203) then
        tmp = (x / a) / y
    else if (b <= 4d-32) then
        tmp = t_1
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 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 / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -3.4e-17) {
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y;
	} else if (b <= -3.3e-288) {
		tmp = t_1;
	} else if (b <= 5.5e-203) {
		tmp = (x / a) / y;
	} else if (b <= 4e-32) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -3.4e-17:
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y
	elif b <= -3.3e-288:
		tmp = t_1
	elif b <= 5.5e-203:
		tmp = (x / a) / y
	elif b <= 4e-32:
		tmp = t_1
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -3.4e-17)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x + Float64(x * Float64(b * -0.5))) / a))) / y);
	elseif (b <= -3.3e-288)
		tmp = t_1;
	elseif (b <= 5.5e-203)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4e-32)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -3.4e-17)
		tmp = ((x / a) - (b * ((x + (x * (b * -0.5))) / a))) / y;
	elseif (b <= -3.3e-288)
		tmp = t_1;
	elseif (b <= 5.5e-203)
		tmp = (x / a) / y;
	elseif (b <= 4e-32)
		tmp = t_1;
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e-17], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x + N[(x * N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.3e-288], t$95$1, If[LessEqual[b, 5.5e-203], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4e-32], t$95$1, N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.3999999999999998e-17

   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 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. distribute-neg-in 86.7%

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

      3. neg-mul-1 86.7%

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

      4. sub-neg 86.7%

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

      5. exp-diff 86.7%

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

      6. neg-mul-1 86.7%

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

      7. log-rec 86.7%

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

      8. rem-exp-log 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in b around 0 41.0%

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

   10. Taylor expanded in b around 0 41.0%

       \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) + -1 \cdot \frac{x}{a}\right)} + \frac{x}{a}}{y} \]
   11. Step-by-step derivation

       1. neg-mul-1 41.0%

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

       2. sub-neg 41.0%

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

       3. distribute-rgt-out 48.4%

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

       4. metadata-eval 48.4%

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

       5. associate-*l/ 48.4%

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

       6. metadata-eval 48.4%

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

       7. distribute-rgt-out 48.4%

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

       8. associate-/l* 49.6%

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

       9. associate-*r/ 49.6%

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

       10. div-sub 49.6%

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

   12. Simplified 49.6%

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

   if -3.3999999999999998e-17 < b < -3.29999999999999988e-288 or 5.5000000000000002e-203 < b < 4.00000000000000022e-32

   1. Initial program 96.1%

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

      1. associate-/l* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 91.2%

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

      4. associate-/l* 88.9%

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

      5. *-commutative 88.9%

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

      6. exp-to-pow 88.9%

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

      7. exp-diff 88.9%

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

      8. *-commutative 88.9%

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

      9. exp-to-pow 89.7%

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

      10. sub-neg 89.7%

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

      11. metadata-eval 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in y around 0 64.7%

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

      1. exp-to-pow 65.2%

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

      2. sub-neg 65.2%

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

      3. metadata-eval 65.2%

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

      4. associate-*r/ 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 33.8%

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

   9. Taylor expanded in b around 0 32.5%

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

       1. distribute-lft-out 33.8%

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

       2. *-commutative 33.8%

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

   11. Simplified 33.8%

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

   12. Taylor expanded in b around inf 30.0%

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

       1. associate-/l* 42.3%

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

       2. distribute-lft-out 48.2%

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

   14. Simplified 48.2%

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

   if -3.29999999999999988e-288 < b < 5.5000000000000002e-203

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. exp-to-pow 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in t around 0 49.7%

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

   if 4.00000000000000022e-32 < b

   1. Initial program 99.9%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 72.5%

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

      4. associate-/l* 72.5%

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

      5. *-commutative 72.5%

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

      6. exp-to-pow 72.5%

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

      7. exp-diff 62.4%

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

      8. *-commutative 62.4%

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

      9. exp-to-pow 62.4%

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

      10. sub-neg 62.4%

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

      11. metadata-eval 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around 0 66.7%

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

      1. exp-to-pow 66.9%

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

      2. sub-neg 66.9%

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

      3. metadata-eval 66.9%

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

      4. associate-*r/ 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around 0 73.0%

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

   9. Taylor expanded in b around 0 51.9%

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

       1. *-commutative 51.9%

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

   11. Simplified 51.9%

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

   12. Taylor expanded in y around 0 58.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x + x \cdot \left(b \cdot -0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-288}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -0.0035:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -0.0035)
     (/ (- x (* b (+ x (* b (* x -0.5))))) (* y a))
     (if (<= b -2.05e-284)
       t_1
       (if (<= b 3.1e-202)
         (/ (/ x a) y)
         (if (<= b 1e-30)
           t_1
           (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -0.0035) {
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	} else if (b <= -2.05e-284) {
		tmp = t_1;
	} else if (b <= 3.1e-202) {
		tmp = (x / a) / y;
	} else if (b <= 1e-30) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 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 / (b * (a * (y + (y / b))))
    if (b <= (-0.0035d0)) then
        tmp = (x - (b * (x + (b * (x * (-0.5d0)))))) / (y * a)
    else if (b <= (-2.05d-284)) then
        tmp = t_1
    else if (b <= 3.1d-202) then
        tmp = (x / a) / y
    else if (b <= 1d-30) then
        tmp = t_1
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 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 / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -0.0035) {
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	} else if (b <= -2.05e-284) {
		tmp = t_1;
	} else if (b <= 3.1e-202) {
		tmp = (x / a) / y;
	} else if (b <= 1e-30) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -0.0035:
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a)
	elif b <= -2.05e-284:
		tmp = t_1
	elif b <= 3.1e-202:
		tmp = (x / a) / y
	elif b <= 1e-30:
		tmp = t_1
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -0.0035)
		tmp = Float64(Float64(x - Float64(b * Float64(x + Float64(b * Float64(x * -0.5))))) / Float64(y * a));
	elseif (b <= -2.05e-284)
		tmp = t_1;
	elseif (b <= 3.1e-202)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 1e-30)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -0.0035)
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	elseif (b <= -2.05e-284)
		tmp = t_1;
	elseif (b <= 3.1e-202)
		tmp = (x / a) / y;
	elseif (b <= 1e-30)
		tmp = t_1;
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.0035], N[(N[(x - N[(b * N[(x + N[(b * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.05e-284], t$95$1, If[LessEqual[b, 3.1e-202], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1e-30], t$95$1, N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.00350000000000000007

   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 90.7%

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

      1. +-commutative 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in y around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. distribute-neg-in 89.1%

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

      3. neg-mul-1 89.1%

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

      4. sub-neg 89.1%

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

      5. exp-diff 89.2%

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

      6. neg-mul-1 89.2%

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

      7. log-rec 89.2%

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

      8. rem-exp-log 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in b around 0 41.2%

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

   10. Taylor expanded in a around 0 49.0%

       \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot x + 0.5 \cdot x\right)\right) - x\right)}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-*r* 49.0%

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

       2. neg-mul-1 49.0%

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

       3. distribute-rgt-out 49.0%

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

       4. metadata-eval 49.0%

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

       5. *-commutative 49.0%

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

   12. Simplified 49.0%

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

   if -0.00350000000000000007 < b < -2.04999999999999999e-284 or 3.1e-202 < b < 1e-30

   1. Initial program 96.3%

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

      1. associate-/l* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 91.5%

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

      4. associate-/l* 89.3%

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

      5. *-commutative 89.3%

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

      6. exp-to-pow 89.3%

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

      7. exp-diff 89.3%

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

      8. *-commutative 89.3%

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

      9. exp-to-pow 90.0%

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

      10. sub-neg 90.0%

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

      11. metadata-eval 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in y around 0 63.7%

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

      1. exp-to-pow 64.2%

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

      2. sub-neg 64.2%

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

      3. metadata-eval 64.2%

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

      4. associate-*r/ 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in t around 0 32.9%

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

   9. Taylor expanded in b around 0 31.6%

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

       1. distribute-lft-out 32.9%

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

       2. *-commutative 32.9%

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

   11. Simplified 32.9%

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

   12. Taylor expanded in b around inf 29.1%

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

       1. associate-/l* 41.1%

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

       2. distribute-lft-out 46.7%

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

   14. Simplified 46.7%

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

   if -2.04999999999999999e-284 < b < 3.1e-202

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 74.8%

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

   4. Taylor expanded in b around 0 74.8%

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

      1. exp-to-pow 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

      4. +-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in t around 0 49.7%

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

   if 1e-30 < b

   1. Initial program 99.9%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 72.5%

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

      4. associate-/l* 72.5%

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

      5. *-commutative 72.5%

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

      6. exp-to-pow 72.5%

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

      7. exp-diff 62.4%

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

      8. *-commutative 62.4%

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

      9. exp-to-pow 62.4%

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

      10. sub-neg 62.4%

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

      11. metadata-eval 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around 0 66.7%

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

      1. exp-to-pow 66.9%

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

      2. sub-neg 66.9%

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

      3. metadata-eval 66.9%

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

      4. associate-*r/ 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around 0 73.0%

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

   9. Taylor expanded in b around 0 51.9%

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

       1. *-commutative 51.9%

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

   11. Simplified 51.9%

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

   12. Taylor expanded in y around 0 58.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0035:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 10^{-30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.4% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{a}\\ t_2 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+97}:\\ \;\;\;\;t\_2 \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x y) a)) (t_2 (/ (/ x a) y)))
   (if (<= b -1.55e+97)
     (* t_2 (- (- -1.0) b))
     (if (<= b -8.2e-287)
       t_1
       (if (<= b 1.9e-206) t_2 (if (<= b 4.4e+39) t_1 (/ x (* y (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) / a;
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -1.55e+97) {
		tmp = t_2 * (-(-1.0) - b);
	} else if (b <= -8.2e-287) {
		tmp = t_1;
	} else if (b <= 1.9e-206) {
		tmp = t_2;
	} else if (b <= 4.4e+39) {
		tmp = t_1;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) / a
    t_2 = (x / a) / y
    if (b <= (-1.55d+97)) then
        tmp = t_2 * (-(-1.0d0) - b)
    else if (b <= (-8.2d-287)) then
        tmp = t_1
    else if (b <= 1.9d-206) then
        tmp = t_2
    else if (b <= 4.4d+39) then
        tmp = t_1
    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 / y) / a;
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -1.55e+97) {
		tmp = t_2 * (-(-1.0) - b);
	} else if (b <= -8.2e-287) {
		tmp = t_1;
	} else if (b <= 1.9e-206) {
		tmp = t_2;
	} else if (b <= 4.4e+39) {
		tmp = t_1;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) / a
	t_2 = (x / a) / y
	tmp = 0
	if b <= -1.55e+97:
		tmp = t_2 * (-(-1.0) - b)
	elif b <= -8.2e-287:
		tmp = t_1
	elif b <= 1.9e-206:
		tmp = t_2
	elif b <= 4.4e+39:
		tmp = t_1
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) / a)
	t_2 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.55e+97)
		tmp = Float64(t_2 * Float64(Float64(-(-1.0)) - b));
	elseif (b <= -8.2e-287)
		tmp = t_1;
	elseif (b <= 1.9e-206)
		tmp = t_2;
	elseif (b <= 4.4e+39)
		tmp = t_1;
	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 / y) / a;
	t_2 = (x / a) / y;
	tmp = 0.0;
	if (b <= -1.55e+97)
		tmp = t_2 * (-(-1.0) - b);
	elseif (b <= -8.2e-287)
		tmp = t_1;
	elseif (b <= 1.9e-206)
		tmp = t_2;
	elseif (b <= 4.4e+39)
		tmp = t_1;
	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 / y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.55e+97], N[(t$95$2 * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-287], t$95$1, If[LessEqual[b, 1.9e-206], t$95$2, If[LessEqual[b, 4.4e+39], t$95$1, N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.54999999999999991e97

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 87.5%

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

      5. *-commutative 87.5%

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

      6. exp-to-pow 87.5%

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

      7. exp-diff 67.5%

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

      8. *-commutative 67.5%

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

      9. exp-to-pow 67.5%

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

      10. sub-neg 67.5%

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

      11. metadata-eval 67.5%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in y around 0 70.0%

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

      1. exp-to-pow 70.0%

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

      2. sub-neg 70.0%

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

      3. metadata-eval 70.0%

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

      4. associate-*r/ 77.5%

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

   7. Simplified 77.5%

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

      1. unpow-prod-up 77.5%

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

      2. unpow-1 77.5%

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

   9. Applied egg-rr 77.5%

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

       1. associate-*r/ 77.5%

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

       2. *-rgt-identity 77.5%

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

   11. Simplified 77.5%

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

   12. Taylor expanded in t around 0 92.6%

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

       1. *-lft-identity 92.6%

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

       2. times-frac 92.6%

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

       3. associate-*l/ 92.6%

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

       4. *-lft-identity 92.6%

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

       5. associate-/r* 85.1%

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

   14. Simplified 85.1%

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

   15. Taylor expanded in b around 0 42.1%

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

       1. mul-1-neg 42.1%

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

       2. remove-double-neg 42.1%

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

       3. distribute-neg-out 42.1%

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

       4. associate-/l* 37.5%

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

       5. mul-1-neg 37.5%

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

       6. distribute-rgt-out 37.5%

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

       7. associate-/r* 37.5%

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

   17. Simplified 37.5%

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

   if -1.54999999999999991e97 < b < -8.2000000000000004e-287 or 1.90000000000000001e-206 < b < 4.4000000000000003e39

   1. Initial program 97.2%

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

      1. associate-/l* 97.3%

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

      2. associate--l+ 97.3%

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

      3. exp-sum 86.5%

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

      4. associate-/l* 84.9%

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

      5. *-commutative 84.9%

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

      6. exp-to-pow 84.9%

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

      7. exp-diff 83.4%

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

      8. *-commutative 83.4%

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

      9. exp-to-pow 83.9%

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

      10. sub-neg 83.9%

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

      11. metadata-eval 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. exp-to-pow 69.1%

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

      2. sub-neg 69.1%

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

      3. metadata-eval 69.1%

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

      4. associate-*r/ 70.0%

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

   7. Simplified 70.0%

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

      1. unpow-prod-up 70.0%

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

      2. unpow-1 70.0%

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

   9. Applied egg-rr 70.0%

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

       1. associate-*r/ 70.0%

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

       2. *-rgt-identity 70.0%

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

   11. Simplified 70.0%

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

   12. Taylor expanded in t around 0 43.9%

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

       1. *-lft-identity 43.9%

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

       2. times-frac 48.9%

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

       3. associate-*l/ 49.0%

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

       4. *-lft-identity 49.0%

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

       5. associate-/r* 45.0%

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

   14. Simplified 45.0%

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

   15. Taylor expanded in b around 0 34.7%

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

   if -8.2000000000000004e-287 < b < 1.90000000000000001e-206

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 73.6%

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

   4. Taylor expanded in b around 0 73.6%

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

      1. exp-to-pow 75.2%

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

      2. sub-neg 75.2%

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

      3. metadata-eval 75.2%

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

      4. +-commutative 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in t around 0 46.5%

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

   if 4.4000000000000003e39 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 72.7%

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

      4. associate-/l* 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

      7. exp-diff 60.0%

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

      8. *-commutative 60.0%

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

      9. exp-to-pow 60.0%

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

      10. sub-neg 60.0%

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

      11. metadata-eval 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in y around 0 63.9%

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

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 69.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 80.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.0%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 42.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 42.0%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 42.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 42.0%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 42.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

       2. *-commutative 42.0%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot b\right) \cdot a}} \]

       3. associate-*l* 47.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(b \cdot a\right)}} \]

   14. Simplified 47.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(b \cdot a\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-206}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.2% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-288} \lor \neg \left(b \leq 3.1 \cdot 10^{-202}\right):\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e-16)
   (/ (- (/ x a) (* b (/ x a))) y)
   (if (or (<= b -2.2e-288) (not (<= b 3.1e-202)))
     (/ x (* b (* a (+ y (/ y b)))))
     (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e-16) {
		tmp = ((x / a) - (b * (x / a))) / y;
	} else if ((b <= -2.2e-288) || !(b <= 3.1e-202)) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.05d-16)) then
        tmp = ((x / a) - (b * (x / a))) / y
    else if ((b <= (-2.2d-288)) .or. (.not. (b <= 3.1d-202))) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e-16) {
		tmp = ((x / a) - (b * (x / a))) / y;
	} else if ((b <= -2.2e-288) || !(b <= 3.1e-202)) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e-16:
		tmp = ((x / a) - (b * (x / a))) / y
	elif (b <= -2.2e-288) or not (b <= 3.1e-202):
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e-16)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(x / a))) / y);
	elseif ((b <= -2.2e-288) || !(b <= 3.1e-202))
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.05e-16)
		tmp = ((x / a) - (b * (x / a))) / y;
	elseif ((b <= -2.2e-288) || ~((b <= 3.1e-202)))
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e-16], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[b, -2.2e-288], N[Not[LessEqual[b, 3.1e-202]], $MachinePrecision]], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0500000000000001e-16

   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 91.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 91.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 91.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 91.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 91.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 86.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \frac{x \cdot e^{-\color{blue}{\left(\log a + b\right)}}}{y} \]

      2. distribute-neg-in 86.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(-\log a\right) + \left(-b\right)}}}{y} \]

      3. neg-mul-1 86.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot \log a} + \left(-b\right)}}{y} \]

      4. sub-neg 86.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot \log a - b}}}{y} \]

      5. exp-diff 86.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}}}{y} \]

      6. neg-mul-1 86.7%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{-\log a}}}{e^{b}}}{y} \]

      7. log-rec 86.7%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}}}{y} \]

      8. rem-exp-log 86.8%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

   8. Simplified 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 38.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 38.3%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 38.3%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 38.3%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 36.8%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 36.8%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   if -1.0500000000000001e-16 < b < -2.2000000000000002e-288 or 3.1e-202 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 66.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 66.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 66.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 69.2%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.2%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 34.9%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 34.9%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 34.9%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 32.1%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 39.0%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 42.2%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 42.2%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if -2.2000000000000002e-288 < b < 3.1e-202

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   4. Taylor expanded in b around 0 74.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. exp-to-pow 76.6%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 76.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 76.6%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

      4. +-commutative 76.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(-1 + t\right)}}}{y} \]

   6. Simplified 76.6%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(-1 + t\right)}}}{y} \]

   7. Taylor expanded in t around 0 49.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-288} \lor \neg \left(b \leq 3.1 \cdot 10^{-202}\right):\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{-16}:\\ \;\;\;\;t\_1 \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq -3.75 \cdot 10^{-289} \lor \neg \left(b \leq 7.6 \cdot 10^{-203}\right):\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -1.1e-16)
     (* t_1 (- (- -1.0) b))
     (if (or (<= b -3.75e-289) (not (<= b 7.6e-203)))
       (/ x (* b (* a (+ y (/ y b)))))
       t_1))))

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 <= -1.1e-16) {
		tmp = t_1 * (-(-1.0) - b);
	} else if ((b <= -3.75e-289) || !(b <= 7.6e-203)) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-1.1d-16)) then
        tmp = t_1 * (-(-1.0d0) - b)
    else if ((b <= (-3.75d-289)) .or. (.not. (b <= 7.6d-203))) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.1e-16) {
		tmp = t_1 * (-(-1.0) - b);
	} else if ((b <= -3.75e-289) || !(b <= 7.6e-203)) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -1.1e-16:
		tmp = t_1 * (-(-1.0) - b)
	elif (b <= -3.75e-289) or not (b <= 7.6e-203):
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.1e-16)
		tmp = Float64(t_1 * Float64(Float64(-(-1.0)) - b));
	elseif ((b <= -3.75e-289) || !(b <= 7.6e-203))
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = t_1;
	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 <= -1.1e-16)
		tmp = t_1 * (-(-1.0) - b);
	elseif ((b <= -3.75e-289) || ~((b <= 7.6e-203)))
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = t_1;
	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, -1.1e-16], N[(t$95$1 * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -3.75e-289], N[Not[LessEqual[b, 7.6e-203]], $MachinePrecision]], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e-16

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 70.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 70.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 71.7%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 71.7%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 71.7%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 76.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 76.3%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

      2. unpow-1 76.3%

         \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

   9. Applied egg-rr 76.3%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 76.3%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

       2. *-rgt-identity 76.3%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

   11. Simplified 76.3%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

   12. Taylor expanded in t around 0 85.5%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. *-lft-identity 85.5%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

       2. times-frac 85.5%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

       3. associate-*l/ 85.5%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       4. *-lft-identity 85.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

       5. associate-/r* 76.4%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

   14. Simplified 76.4%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   15. Taylor expanded in b around 0 32.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   16. Step-by-step derivation

       1. mul-1-neg 32.7%

          \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

       2. remove-double-neg 32.7%

          \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. distribute-neg-out 32.7%

          \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       4. associate-/l* 28.5%

          \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} + \left(-\frac{x}{a \cdot y}\right)\right) \]

       5. mul-1-neg 28.5%

          \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} + \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       6. distribute-rgt-out 28.5%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

       7. associate-/r* 29.8%

          \[\leadsto -\color{blue}{\frac{\frac{x}{a}}{y}} \cdot \left(b + -1\right) \]

   17. Simplified 29.8%

       \[\leadsto \color{blue}{-\frac{\frac{x}{a}}{y} \cdot \left(b + -1\right)} \]

   if -1.1e-16 < b < -3.74999999999999999e-289 or 7.6000000000000005e-203 < b

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 66.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 66.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 66.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 69.2%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.2%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 34.9%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 34.9%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 34.9%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 32.1%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 39.0%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 42.2%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 42.2%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if -3.74999999999999999e-289 < b < 7.6000000000000005e-203

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   4. Taylor expanded in b around 0 74.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. exp-to-pow 76.6%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 76.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 76.6%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

      4. +-commutative 76.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(-1 + t\right)}}}{y} \]

   6. Simplified 76.6%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(-1 + t\right)}}}{y} \]

   7. Taylor expanded in t around 0 49.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq -3.75 \cdot 10^{-289} \lor \neg \left(b \leq 7.6 \cdot 10^{-203}\right):\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.4% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 10^{-32}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.4e-159)
   (/ (- (/ x y) (* x (/ b y))) a)
   (if (<= b 1e-32)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e-159) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= 1e-32) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.4d-159)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= 1d-32) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e-159) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= 1e-32) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.4e-159:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= 1e-32:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.4e-159)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= 1e-32)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.4e-159)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= 1e-32)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.4e-159], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1e-32], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.39999999999999984e-159

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 75.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 75.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 75.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 75.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 75.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 69.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 72.7%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

      2. unpow-1 72.7%

         \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

   9. Applied egg-rr 72.7%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 72.7%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

       2. *-rgt-identity 72.7%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

   11. Simplified 72.7%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

   12. Taylor expanded in t around 0 69.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. *-lft-identity 69.2%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

       2. times-frac 72.0%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

       3. associate-*l/ 72.0%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       4. *-lft-identity 72.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

       5. associate-/r* 65.8%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

   14. Simplified 65.8%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   15. Taylor expanded in b around 0 40.5%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}}}{a} \]
   16. Step-by-step derivation

       1. +-commutative 40.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}}}{a} \]

       2. mul-1-neg 40.5%

          \[\leadsto \frac{\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}}{a} \]

       3. unsub-neg 40.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}}}{a} \]

       4. *-commutative 40.5%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}}{a} \]

       5. associate-/l* 40.5%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{x \cdot \frac{b}{y}}}{a} \]

   17. Simplified 40.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{y} - x \cdot \frac{b}{y}}}{a} \]

   if -3.39999999999999984e-159 < b < 1.00000000000000006e-32

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 91.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 88.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 88.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 88.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 88.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 88.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 88.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 88.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 88.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 69.7%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 69.7%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 69.7%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 67.8%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 67.8%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 35.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.0%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 35.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 35.0%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 35.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 31.9%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 41.4%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 45.9%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 45.9%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 1.00000000000000006e-32 < b

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 72.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 72.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 72.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 72.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 62.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 62.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 62.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 62.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 62.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 66.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 66.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 66.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 71.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 71.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 73.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 51.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 51.9%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]

   11. Simplified 51.9%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}} \]

   12. Taylor expanded in y around 0 58.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 10^{-32}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.6% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5e-148)
   (/ (- (/ x y) (* x (/ b y))) a)
   (/ 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-148) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} 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-148)) then
        tmp = ((x / y) - (x * (b / y))) / a
    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-148) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} 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-148:
		tmp = ((x / y) - (x * (b / y))) / a
	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-148)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	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-148)
		tmp = ((x / y) - (x * (b / y))) / a;
	else
		tmp = x / (b * (a * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5e-148], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $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 < -1.49999999999999999e-148

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 75.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 75.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 75.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 75.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 75.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 69.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 72.7%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

      2. unpow-1 72.7%

         \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

   9. Applied egg-rr 72.7%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 72.7%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

       2. *-rgt-identity 72.7%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

   11. Simplified 72.7%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

   12. Taylor expanded in t around 0 69.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. *-lft-identity 69.2%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

       2. times-frac 72.0%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

       3. associate-*l/ 72.0%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       4. *-lft-identity 72.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

       5. associate-/r* 65.8%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

   14. Simplified 65.8%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   15. Taylor expanded in b around 0 40.5%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}}}{a} \]
   16. Step-by-step derivation

       1. +-commutative 40.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}}}{a} \]

       2. mul-1-neg 40.5%

          \[\leadsto \frac{\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}}{a} \]

       3. unsub-neg 40.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}}}{a} \]

       4. *-commutative 40.5%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}}{a} \]

       5. associate-/l* 40.5%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{x \cdot \frac{b}{y}}}{a} \]

   17. Simplified 40.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{y} - x \cdot \frac{b}{y}}}{a} \]

   if -1.49999999999999999e-148 < b

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 76.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 76.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 68.5%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 68.5%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 68.5%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 69.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 51.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 35.5%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 35.5%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 35.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 33.2%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 38.6%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 41.1%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 41.1%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 41.3% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.2e-16)
   (* (/ (/ x a) y) (- (- -1.0) b))
   (/ x (* a (* b (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.2e-16) {
		tmp = ((x / a) / y) * (-(-1.0) - b);
	} else {
		tmp = x / (a * (b * (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 <= (-4.2d-16)) then
        tmp = ((x / a) / y) * (-(-1.0d0) - b)
    else
        tmp = x / (a * (b * (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 <= -4.2e-16) {
		tmp = ((x / a) / y) * (-(-1.0) - b);
	} else {
		tmp = x / (a * (b * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.2e-16:
		tmp = ((x / a) / y) * (-(-1.0) - b)
	else:
		tmp = x / (a * (b * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.2e-16)
		tmp = Float64(Float64(Float64(x / a) / y) * Float64(Float64(-(-1.0)) - b));
	else
		tmp = Float64(x / Float64(a * Float64(b * 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 <= -4.2e-16)
		tmp = ((x / a) / y) * (-(-1.0) - b);
	else
		tmp = x / (a * (b * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.2e-16], N[(N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision] * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(b * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2000000000000002e-16

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 70.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 70.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 71.7%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 71.7%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 71.7%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 76.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 76.3%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

      2. unpow-1 76.3%

         \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

   9. Applied egg-rr 76.3%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 76.3%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

       2. *-rgt-identity 76.3%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

   11. Simplified 76.3%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

   12. Taylor expanded in t around 0 85.5%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. *-lft-identity 85.5%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

       2. times-frac 85.5%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

       3. associate-*l/ 85.5%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       4. *-lft-identity 85.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

       5. associate-/r* 76.4%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

   14. Simplified 76.4%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   15. Taylor expanded in b around 0 32.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   16. Step-by-step derivation

       1. mul-1-neg 32.7%

          \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

       2. remove-double-neg 32.7%

          \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. distribute-neg-out 32.7%

          \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       4. associate-/l* 28.5%

          \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} + \left(-\frac{x}{a \cdot y}\right)\right) \]

       5. mul-1-neg 28.5%

          \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} + \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       6. distribute-rgt-out 28.5%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

       7. associate-/r* 29.8%

          \[\leadsto -\color{blue}{\frac{\frac{x}{a}}{y}} \cdot \left(b + -1\right) \]

   17. Simplified 29.8%

       \[\leadsto \color{blue}{-\frac{\frac{x}{a}}{y} \cdot \left(b + -1\right)} \]

   if -4.2000000000000002e-16 < b

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 78.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 78.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 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. exp-to-pow 67.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 68.6%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 68.6%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 48.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 35.1%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 35.1%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 35.1%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 40.6%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.4e+40) (/ (/ x y) a) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.4e+40) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.4d+40) then
        tmp = (x / y) / a
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.4e+40) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.4e+40:
		tmp = (x / y) / a
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.4e+40)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.4e+40)
		tmp = (x / y) / a;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.4e+40], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.4000000000000001e40

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 87.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 70.3%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 70.3%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 70.3%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 71.0%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 71.0%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

      2. unpow-1 71.0%

         \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

   9. Applied egg-rr 71.0%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 71.0%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

       2. *-rgt-identity 71.0%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

   11. Simplified 71.0%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

   12. Taylor expanded in t around 0 52.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. *-lft-identity 52.2%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

       2. times-frac 55.0%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

       3. associate-*l/ 55.0%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       4. *-lft-identity 55.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

       5. associate-/r* 50.9%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

   14. Simplified 50.9%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   15. Taylor expanded in b around 0 31.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if 1.4000000000000001e40 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 72.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 72.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 72.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 69.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 80.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.0%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 42.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 42.0%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 42.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 42.0%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 42.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

       2. *-commutative 42.0%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot b\right) \cdot a}} \]

       3. associate-*l* 47.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(b \cdot a\right)}} \]

   14. Simplified 47.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(b \cdot a\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.8% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 9.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 9.8e+39) (/ (/ x y) a) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 9.8e+39) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 9.8d+39) then
        tmp = (x / y) / a
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 9.8e+39) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 9.8e+39:
		tmp = (x / y) / a
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 9.8e+39)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 9.8e+39)
		tmp = (x / y) / a;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 9.8e+39], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 9.79999999999999974e39

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 87.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 70.3%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 70.3%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 70.3%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 71.0%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 71.0%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

      2. unpow-1 71.0%

         \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

   9. Applied egg-rr 71.0%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 71.0%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

       2. *-rgt-identity 71.0%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

   11. Simplified 71.0%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

   12. Taylor expanded in t around 0 52.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. *-lft-identity 52.2%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

       2. times-frac 55.0%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

       3. associate-*l/ 55.0%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       4. *-lft-identity 55.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

       5. associate-/r* 50.9%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

   14. Simplified 50.9%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   15. Taylor expanded in b around 0 31.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if 9.79999999999999974e39 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 72.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 72.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 72.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 72.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 69.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 80.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.0%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 42.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 42.0%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 42.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 42.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 42.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 42.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 31.0% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{a} \end{array} \]

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(Float64(x / 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[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.0%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.0%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 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* 82.8%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 82.8%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 82.8%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 76.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 76.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 76.6%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 76.6%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 76.6%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 76.6%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 68.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. exp-to-pow 68.9%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   2. sub-neg 68.9%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   3. metadata-eval 68.9%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   4. associate-*r/ 70.6%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

7. Simplified 70.6%

   \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]
8. Step-by-step derivation

   1. unpow-prod-up 70.7%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y \cdot e^{b}} \]

   2. unpow-1 70.7%

      \[\leadsto x \cdot \frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y \cdot e^{b}} \]

9. Applied egg-rr 70.7%

   \[\leadsto x \cdot \frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y \cdot e^{b}} \]
10. Step-by-step derivation

    1. associate-*r/ 70.7%

       \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y \cdot e^{b}} \]

    2. *-rgt-identity 70.7%

       \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t}}}{a}}{y \cdot e^{b}} \]

11. Simplified 70.7%

    \[\leadsto x \cdot \frac{\color{blue}{\frac{{a}^{t}}{a}}}{y \cdot e^{b}} \]

12. Taylor expanded in t around 0 58.2%

    \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
13. Step-by-step derivation

    1. *-lft-identity 58.2%

       \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

    2. times-frac 60.4%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

    3. associate-*l/ 60.4%

       \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

    4. *-lft-identity 60.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

    5. associate-/r* 54.1%

       \[\leadsto \frac{\color{blue}{\frac{\frac{x}{y}}{e^{b}}}}{a} \]

14. Simplified 54.1%

    \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

15. Taylor expanded in b around 0 27.1%

    \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]
16. Add Preprocessing

Alternative 22: 31.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 78.2%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

4. Taylor expanded in b around 0 54.5%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
5. Step-by-step derivation

   1. exp-to-pow 54.9%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

   2. sub-neg 54.9%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

   3. metadata-eval 54.9%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

   4. +-commutative 54.9%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(-1 + t\right)}}}{y} \]

6. Simplified 54.9%

   \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(-1 + t\right)}}}{y} \]

7. Taylor expanded in t around 0 25.5%

   \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
8. Add Preprocessing

Alternative 23: 31.3% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.0%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.0%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 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* 82.8%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 82.8%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 82.8%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 76.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 76.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 76.6%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 76.6%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 76.6%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 76.6%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 68.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. exp-to-pow 68.9%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   2. sub-neg 68.9%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   3. metadata-eval 68.9%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   4. associate-*r/ 70.6%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

7. Simplified 70.6%

   \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

8. Taylor expanded in t around 0 58.2%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 24.2%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 24.2%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024088 
(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))