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

Percentage Accurate: 98.2% → 98.2%

Time: 22.3s

Alternatives: 20

Speedup: 1.0×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% 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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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)) + (log(a) * (t + (-1.0d0)))) - 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)) + (Math.log(a) * (t + -1.0))) - b))) / y;
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 96.6%

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

3. Final simplification 96.6%

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

Alternative 2: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.45e+92)
   (/ (* x (/ (pow z y) a)) y)
   (if (<= y 5.8e+53)
     (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)
     (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+92) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (y <= 5.8e+53) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.45d+92)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (y <= 5.8d+53) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+92) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (y <= 5.8e+53) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.45e+92:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif y <= 5.8e+53:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.45e+92)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (y <= 5.8e+53)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.45e+92)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (y <= 5.8e+53)
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.45e+92], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 5.8e+53], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000001e92

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in b around 0 92.0%

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

      1. exp-diff 92.0%

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

      2. *-commutative 92.0%

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

      3. exp-to-pow 92.0%

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

      4. rem-exp-log 92.0%

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

   8. Simplified 92.0%

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

   if -2.4500000000000001e92 < y < 5.8000000000000004e53

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0 90.6%

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

   if 5.8000000000000004e53 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 96.3%

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

      1. +-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. unsub-neg 96.3%

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

   5. Simplified 96.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+186} \lor \neg \left(b \leq 90000000000000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{{z}^{y}}{y} \cdot {a}^{\left(t + -1\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+186) (not (<= b 90000000000000.0)))
   (/ x (* a (* y (exp b))))
   (* x (* (/ (pow z y) y) (pow a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+186) || !(b <= 90000000000000.0)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * ((pow(z, y) / y) * pow(a, (t + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.5d+186)) .or. (.not. (b <= 90000000000000.0d0))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (((z ** y) / y) * (a ** (t + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+186) || !(b <= 90000000000000.0)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * ((Math.pow(z, y) / y) * Math.pow(a, (t + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+186) or not (b <= 90000000000000.0):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * ((math.pow(z, y) / y) * math.pow(a, (t + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+186) || !(b <= 90000000000000.0))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / y) * (a ^ Float64(t + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+186) || ~((b <= 90000000000000.0)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (((z ^ y) / y) * (a ^ (t + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+186], N[Not[LessEqual[b, 90000000000000.0]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.4999999999999998e186 or 9e13 < 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 77.5%

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

      4. associate-/l* 77.5%

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

      5. *-commutative 77.5%

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

      6. exp-to-pow 77.5%

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

      7. exp-diff 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 t around 0 76.3%

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

   6. Taylor expanded in y around 0 90.2%

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

   if -7.4999999999999998e186 < b < 9e13

   1. Initial program 95.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 81.6%

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

      4. associate-/l* 79.4%

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

      5. *-commutative 79.4%

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

      6. exp-to-pow 79.4%

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

      7. exp-diff 74.8%

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

      8. *-commutative 74.8%

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

      9. exp-to-pow 75.9%

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

      10. sub-neg 75.9%

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

      11. metadata-eval 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in b around 0 81.2%

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

      1. associate-/l* 81.2%

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

      2. exp-to-pow 82.1%

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

      3. sub-neg 82.1%

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

      4. metadata-eval 82.1%

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

   7. Simplified 82.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+186} \lor \neg \left(b \leq 90000000000000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{{z}^{y}}{y} \cdot {a}^{\left(t + -1\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+96} \lor \neg \left(y \leq 1.05 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.65e+96) (not (<= y 1.05e+54)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.65e+96) || !(y <= 1.05e+54)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - 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 <= (-3.65d+96)) .or. (.not. (y <= 1.05d+54))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - 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 <= -3.65e+96) || !(y <= 1.05e+54)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.65e+96) or not (y <= 1.05e+54):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.65e+96) || !(y <= 1.05e+54))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.65e+96) || ~((y <= 1.05e+54)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.65e+96], N[Not[LessEqual[y, 1.05e+54]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.65e96 or 1.04999999999999993e54 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.2%

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

      1. +-commutative 94.2%

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

      2. mul-1-neg 94.2%

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

      3. unsub-neg 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in b around 0 90.3%

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

      1. exp-diff 90.3%

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

      2. *-commutative 90.3%

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

      3. exp-to-pow 90.3%

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

      4. rem-exp-log 90.3%

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

   8. Simplified 90.3%

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

   if -3.65e96 < y < 1.04999999999999993e54

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0 90.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+96} \lor \neg \left(y \leq 1.05 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+60} \lor \neg \left(y \leq 0.09\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.8e+60) (not (<= y 0.09)))
   (/ (* x (/ (pow z y) a)) y)
   (* x (/ (pow a t) (* y (* a (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e+60) || !(y <= 0.09)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * (pow(a, t) / (y * (a * 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 <= (-2.8d+60)) .or. (.not. (y <= 0.09d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x * ((a ** t) / (y * (a * 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 <= -2.8e+60) || !(y <= 0.09)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x * (Math.pow(a, t) / (y * (a * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.8e+60) or not (y <= 0.09):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x * (math.pow(a, t) / (y * (a * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.8e+60) || !(y <= 0.09))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64((a ^ t) / Float64(y * Float64(a * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.8e+60) || ~((y <= 0.09)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x * ((a ^ t) / (y * (a * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.8e+60], N[Not[LessEqual[y, 0.09]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e60 or 0.089999999999999997 < 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 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in b around 0 85.3%

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

      1. exp-diff 85.2%

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

      2. *-commutative 85.2%

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

      3. exp-to-pow 85.2%

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

      4. rem-exp-log 85.3%

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

   8. Simplified 85.3%

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

   if -2.8e60 < y < 0.089999999999999997

   1. Initial program 93.5%

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

      1. associate-/l* 98.4%

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

      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 92.5%

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

      4. associate-/l* 92.5%

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

      5. *-commutative 92.5%

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

      6. exp-to-pow 92.5%

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

      7. exp-diff 81.3%

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

      8. *-commutative 81.3%

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

      9. exp-to-pow 82.6%

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

      10. sub-neg 82.6%

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

      11. metadata-eval 82.6%

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

   3. Simplified 82.6%

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

      1. associate-/l/ 82.6%

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

      2. unpow-prod-up 82.8%

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

      3. associate-/l* 78.4%

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

      4. unpow-1 78.4%

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

   6. Applied egg-rr 78.4%

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

      1. associate-*r/ 82.8%

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

      2. times-frac 82.0%

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

      3. associate-*l/ 82.8%

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

      4. associate-/l/ 82.8%

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

      5. associate-*r/ 82.8%

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

      6. *-rgt-identity 82.8%

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

   8. Simplified 82.8%

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

   9. Taylor expanded in y around 0 81.3%

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

       1. associate-*r* 77.6%

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

       2. *-commutative 77.6%

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

       3. associate-*r* 81.3%

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

   11. Simplified 81.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+60} \lor \neg \left(y \leq 0.09\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{z}^{y}}{y \cdot a}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq 60000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow z y) (* y a)))) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -1.6e-8)
     t_2
     (if (<= b -3.1e-171)
       t_1
       (if (<= b 8.6e-239)
         (* x (/ (pow a t) (* y a)))
         (if (<= b 60000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(z, y) / (y * a));
	double t_2 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -1.6e-8) {
		tmp = t_2;
	} else if (b <= -3.1e-171) {
		tmp = t_1;
	} else if (b <= 8.6e-239) {
		tmp = x * (pow(a, t) / (y * a));
	} else if (b <= 60000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((z ** y) / (y * a))
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-1.6d-8)) then
        tmp = t_2
    else if (b <= (-3.1d-171)) then
        tmp = t_1
    else if (b <= 8.6d-239) then
        tmp = x * ((a ** t) / (y * a))
    else if (b <= 60000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(z, y) / (y * a));
	double t_2 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -1.6e-8) {
		tmp = t_2;
	} else if (b <= -3.1e-171) {
		tmp = t_1;
	} else if (b <= 8.6e-239) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if (b <= 60000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(z, y) / (y * a))
	t_2 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -1.6e-8:
		tmp = t_2
	elif b <= -3.1e-171:
		tmp = t_1
	elif b <= 8.6e-239:
		tmp = x * (math.pow(a, t) / (y * a))
	elif b <= 60000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((z ^ y) / Float64(y * a)))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -1.6e-8)
		tmp = t_2;
	elseif (b <= -3.1e-171)
		tmp = t_1;
	elseif (b <= 8.6e-239)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (b <= 60000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((z ^ y) / (y * a));
	t_2 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -1.6e-8)
		tmp = t_2;
	elseif (b <= -3.1e-171)
		tmp = t_1;
	elseif (b <= 8.6e-239)
		tmp = x * ((a ^ t) / (y * a));
	elseif (b <= 60000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e-8], t$95$2, If[LessEqual[b, -3.1e-171], t$95$1, If[LessEqual[b, 8.6e-239], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 60000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6000000000000001e-8 or 6e4 < 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* 99.9%

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

      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 79.9%

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

      4. associate-/l* 79.9%

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

      5. *-commutative 79.9%

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

      6. exp-to-pow 79.9%

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

      7. exp-diff 62.3%

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

      8. *-commutative 62.3%

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

      9. exp-to-pow 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 t around 0 73.7%

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

   6. Taylor expanded in y around 0 82.7%

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

   if -1.6000000000000001e-8 < b < -3.1e-171 or 8.6000000000000001e-239 < b < 6e4

   1. Initial program 93.5%

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

      1. associate-/l* 98.4%

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

      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 82.4%

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

      4. associate-/l* 81.1%

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

      5. *-commutative 81.1%

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

      6. exp-to-pow 81.1%

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

      7. exp-diff 81.1%

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

      8. *-commutative 81.1%

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

      9. exp-to-pow 82.4%

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

      10. sub-neg 82.4%

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

      11. metadata-eval 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in t around 0 69.0%

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

   6. Taylor expanded in b around 0 69.3%

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

   if -3.1e-171 < b < 8.6000000000000001e-239

   1. Initial program 93.1%

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

      1. associate-/l* 98.1%

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

      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 78.1%

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

      4. associate-/l* 72.1%

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

      5. *-commutative 72.1%

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

      6. exp-to-pow 72.1%

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

      7. exp-diff 72.1%

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

      8. *-commutative 72.1%

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

      9. exp-to-pow 73.6%

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

      10. sub-neg 73.6%

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

      11. metadata-eval 73.6%

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

   3. Simplified 73.6%

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

      1. associate-/l/ 73.6%

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

      2. unpow-prod-up 73.9%

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

      3. associate-/l* 71.9%

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

      4. unpow-1 71.9%

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

   6. Applied egg-rr 71.9%

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

      1. associate-*r/ 73.9%

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

      2. times-frac 73.9%

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

      3. associate-*l/ 73.9%

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

      4. associate-/l/ 73.9%

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

      5. associate-*r/ 73.8%

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

      6. *-rgt-identity 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in y around 0 79.8%

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

       1. associate-*r* 79.8%

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

       2. *-commutative 79.8%

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

       3. associate-*r* 79.8%

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

   11. Simplified 79.8%

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

   12. Taylor expanded in b around 0 79.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq 60000:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e-5)
   (* x (/ (pow a t) (* y a)))
   (if (<= t 4.5e-147)
     (* x (/ (pow z y) (* y a)))
     (if (<= t 8e+50)
       (/ x (* a (* y (exp b))))
       (* (pow a (+ t -1.0)) (/ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e-5) {
		tmp = x * (pow(a, t) / (y * a));
	} else if (t <= 4.5e-147) {
		tmp = x * (pow(z, y) / (y * a));
	} else if (t <= 8e+50) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = pow(a, (t + -1.0)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.35d-5)) then
        tmp = x * ((a ** t) / (y * a))
    else if (t <= 4.5d-147) then
        tmp = x * ((z ** y) / (y * a))
    else if (t <= 8d+50) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (a ** (t + (-1.0d0))) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e-5) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if (t <= 4.5e-147) {
		tmp = x * (Math.pow(z, y) / (y * a));
	} else if (t <= 8e+50) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e-5:
		tmp = x * (math.pow(a, t) / (y * a))
	elif t <= 4.5e-147:
		tmp = x * (math.pow(z, y) / (y * a))
	elif t <= 8e+50:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = math.pow(a, (t + -1.0)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e-5)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (t <= 4.5e-147)
		tmp = Float64(x * Float64((z ^ y) / Float64(y * a)));
	elseif (t <= 8e+50)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.35e-5)
		tmp = x * ((a ^ t) / (y * a));
	elseif (t <= 4.5e-147)
		tmp = x * ((z ^ y) / (y * a));
	elseif (t <= 8e+50)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (a ^ (t + -1.0)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e-5], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-147], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+50], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3499999999999999e-5

   1. Initial program 98.4%

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

      1. associate-/l* 99.6%

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

      2. associate--l+ 99.6%

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

      3. exp-sum 70.8%

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

      4. associate-/l* 70.8%

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

      5. *-commutative 70.8%

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

      6. exp-to-pow 70.8%

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

      7. exp-diff 54.2%

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

      8. *-commutative 54.2%

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

      9. exp-to-pow 54.4%

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

      10. sub-neg 54.4%

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

      11. metadata-eval 54.4%

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

   3. Simplified 54.4%

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

      1. associate-/l/ 54.4%

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

      2. unpow-prod-up 54.5%

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

      3. associate-/l* 54.5%

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

      4. unpow-1 54.5%

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

   6. Applied egg-rr 54.5%

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

      1. associate-*r/ 54.5%

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

      2. times-frac 53.0%

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

      3. associate-*l/ 54.5%

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

      4. associate-/l/ 54.5%

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

      5. associate-*r/ 54.5%

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

      6. *-rgt-identity 54.5%

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

   8. Simplified 54.5%

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

   9. Taylor expanded in y around 0 69.8%

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

       1. associate-*r* 68.3%

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

       2. *-commutative 68.3%

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

       3. associate-*r* 69.8%

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

   11. Simplified 69.8%

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

   12. Taylor expanded in b around 0 79.1%

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

   if -1.3499999999999999e-5 < t < 4.49999999999999973e-147

   1. Initial program 93.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 89.7%

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

      4. associate-/l* 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 85.5%

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

      7. exp-diff 85.5%

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

      8. *-commutative 85.5%

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

      9. exp-to-pow 87.2%

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

      10. sub-neg 87.2%

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

      11. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around 0 87.3%

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

   6. Taylor expanded in b around 0 76.9%

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

   if 4.49999999999999973e-147 < t < 8.0000000000000006e50

   1. Initial program 96.4%

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

      1. associate-/l* 99.0%

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

      2. associate--l+ 99.0%

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

      3. exp-sum 92.9%

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

      4. associate-/l* 92.9%

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

      5. *-commutative 92.9%

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

      6. exp-to-pow 92.9%

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

      7. exp-diff 80.8%

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

      8. *-commutative 80.8%

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

      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 t around 0 87.3%

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

   6. Taylor expanded in y around 0 81.6%

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

   if 8.0000000000000006e50 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.3%

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

   4. Taylor expanded in b around 0 80.9%

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

      1. *-commutative 80.9%

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

      2. exp-to-pow 80.9%

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

      3. sub-neg 80.9%

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

      4. metadata-eval 80.9%

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

      5. associate-*r/ 71.2%

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

      6. +-commutative 71.2%

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

   6. Simplified 71.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-194}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.076:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -1.6e+60)
     t_1
     (if (<= y -1.5e-194)
       (* (pow a (+ t -1.0)) (/ x y))
       (if (<= y 0.076) (/ 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 <= -1.6e+60) {
		tmp = t_1;
	} else if (y <= -1.5e-194) {
		tmp = pow(a, (t + -1.0)) * (x / y);
	} else if (y <= 0.076) {
		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 <= (-1.6d+60)) then
        tmp = t_1
    else if (y <= (-1.5d-194)) then
        tmp = (a ** (t + (-1.0d0))) * (x / y)
    else if (y <= 0.076d0) 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 <= -1.6e+60) {
		tmp = t_1;
	} else if (y <= -1.5e-194) {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	} else if (y <= 0.076) {
		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 <= -1.6e+60:
		tmp = t_1
	elif y <= -1.5e-194:
		tmp = math.pow(a, (t + -1.0)) * (x / y)
	elif y <= 0.076:
		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(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -1.6e+60)
		tmp = t_1;
	elseif (y <= -1.5e-194)
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / y));
	elseif (y <= 0.076)
		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 <= -1.6e+60)
		tmp = t_1;
	elseif (y <= -1.5e-194)
		tmp = (a ^ (t + -1.0)) * (x / y);
	elseif (y <= 0.076)
		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[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.6e+60], t$95$1, If[LessEqual[y, -1.5e-194], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.076], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999995e60 or 0.0759999999999999981 < 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 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in b around 0 85.3%

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

      1. exp-diff 85.2%

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

      2. *-commutative 85.2%

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

      3. exp-to-pow 85.2%

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

      4. rem-exp-log 85.3%

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

   8. Simplified 85.3%

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

   if -1.59999999999999995e60 < y < -1.5e-194

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 91.4%

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

   4. Taylor expanded in b around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. exp-to-pow 82.4%

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

      3. sub-neg 82.4%

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

      4. metadata-eval 82.4%

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

      5. associate-*r/ 83.9%

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

      6. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   if -1.5e-194 < y < 0.0759999999999999981

   1. Initial program 92.5%

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

      1. associate-/l* 98.3%

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

      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 98.3%

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

      4. associate-/l* 98.3%

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

      5. *-commutative 98.3%

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

      6. exp-to-pow 98.3%

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

      7. exp-diff 85.2%

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

      8. *-commutative 85.2%

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

      9. exp-to-pow 86.7%

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

      10. sub-neg 86.7%

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

      11. metadata-eval 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in t around 0 75.9%

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

   6. Taylor expanded in y around 0 76.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-194}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.076:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-252}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 0.082:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -7e+61)
     t_1
     (if (<= y -3.6e-252)
       (/ (* x (pow a (+ t -1.0))) y)
       (if (<= y 0.082) (/ 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 <= -7e+61) {
		tmp = t_1;
	} else if (y <= -3.6e-252) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 0.082) {
		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 <= (-7d+61)) then
        tmp = t_1
    else if (y <= (-3.6d-252)) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 0.082d0) 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 <= -7e+61) {
		tmp = t_1;
	} else if (y <= -3.6e-252) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 0.082) {
		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 <= -7e+61:
		tmp = t_1
	elif y <= -3.6e-252:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 0.082:
		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(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -7e+61)
		tmp = t_1;
	elseif (y <= -3.6e-252)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 0.082)
		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 <= -7e+61)
		tmp = t_1;
	elseif (y <= -3.6e-252)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 0.082)
		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[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -7e+61], t$95$1, If[LessEqual[y, -3.6e-252], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 0.082], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000036e61 or 0.0820000000000000034 < 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 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in b around 0 85.3%

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

      1. exp-diff 85.2%

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

      2. *-commutative 85.2%

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

      3. exp-to-pow 85.2%

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

      4. rem-exp-log 85.3%

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

   8. Simplified 85.3%

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

   if -7.00000000000000036e61 < y < -3.60000000000000023e-252

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0 91.5%

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

   4. Taylor expanded in b around 0 80.8%

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

      1. exp-to-pow 81.5%

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

      2. sub-neg 81.5%

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

      3. metadata-eval 81.5%

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

      4. +-commutative 81.5%

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

   6. Simplified 81.5%

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

   if -3.60000000000000023e-252 < y < 0.0820000000000000034

   1. Initial program 92.6%

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

      1. associate-/l* 98.3%

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

      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 98.3%

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

      4. associate-/l* 98.3%

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

      5. *-commutative 98.3%

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

      6. exp-to-pow 98.3%

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

      7. exp-diff 87.0%

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

      8. *-commutative 87.0%

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

      9. exp-to-pow 88.5%

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

      10. sub-neg 88.5%

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

      11. metadata-eval 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around 0 77.0%

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

   6. Taylor expanded in y around 0 77.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-252}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 0.082:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-20} \lor \neg \left(b \leq 9.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.55e-20) (not (<= b 9.4e-11)))
   (/ x (* a (* y (exp b))))
   (* x (/ (pow a t) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.55e-20) || !(b <= 9.4e-11)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (pow(a, t) / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.55d-20)) .or. (.not. (b <= 9.4d-11))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * ((a ** t) / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.55e-20) || !(b <= 9.4e-11)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(a, t) / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.55e-20) or not (b <= 9.4e-11):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.pow(a, t) / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.55e-20) || !(b <= 9.4e-11))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.55e-20) || ~((b <= 9.4e-11)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * ((a ^ t) / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.55e-20], N[Not[LessEqual[b, 9.4e-11]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.55e-20 or 9.39999999999999985e-11 < 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* 99.9%

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

      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 78.7%

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

      4. associate-/l* 78.7%

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

      5. *-commutative 78.7%

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

      6. exp-to-pow 78.7%

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

      7. exp-diff 62.0%

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

      8. *-commutative 62.0%

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

      9. exp-to-pow 62.1%

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

      10. sub-neg 62.1%

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

      11. metadata-eval 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in t around 0 73.6%

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

   6. Taylor expanded in y around 0 79.9%

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

   if -1.55e-20 < b < 9.39999999999999985e-11

   1. Initial program 93.0%

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

      1. associate-/l* 98.3%

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

      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 82.1%

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

      4. associate-/l* 78.9%

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

      5. *-commutative 78.9%

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

      6. exp-to-pow 78.9%

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

      7. exp-diff 78.9%

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

      8. *-commutative 78.9%

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

      9. exp-to-pow 80.3%

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

      10. sub-neg 80.3%

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

      11. metadata-eval 80.3%

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

   3. Simplified 80.3%

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

      1. associate-/l/ 80.3%

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

      2. unpow-prod-up 80.5%

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

      3. associate-/l* 74.9%

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

      4. unpow-1 74.9%

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

   6. Applied egg-rr 74.9%

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

      1. associate-*r/ 80.5%

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

      2. times-frac 80.5%

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

      3. associate-*l/ 80.5%

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

      4. associate-/l/ 80.5%

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

      5. associate-*r/ 80.5%

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

      6. *-rgt-identity 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in y around 0 65.8%

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

       1. associate-*r* 65.8%

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

       2. *-commutative 65.8%

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

       3. associate-*r* 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in b around 0 65.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-20} \lor \neg \left(b \leq 9.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. associate-/l* 99.1%

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

   2. associate--l+ 99.1%

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

   3. exp-sum 80.3%

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

   4. associate-/l* 78.8%

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

   5. *-commutative 78.8%

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

   6. exp-to-pow 78.8%

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

   7. exp-diff 70.2%

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

   8. *-commutative 70.2%

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

   9. exp-to-pow 70.9%

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

   10. sub-neg 70.9%

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

   11. metadata-eval 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in t around 0 68.8%

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

6. Taylor expanded in y around 0 60.1%

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

7. Final simplification 60.1%

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

Alternative 12: 47.1% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(\frac{\frac{b}{y}}{-a} - \frac{-1}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.5:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+173)
   (* x (- (/ (/ b y) (- a)) (/ -1.0 (* y a))))
   (if (<= b -1.5)
     (/ (* a (- (* y (/ x y)) (* x b))) (* y (* a a)))
     (/
      x
      (*
       a
       (+
        y
        (* b (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+173) {
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	} else if (b <= -1.5) {
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a));
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+173)) then
        tmp = x * (((b / y) / -a) - ((-1.0d0) / (y * a)))
    else if (b <= (-1.5d0)) then
        tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a))
    else
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+173) {
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	} else if (b <= -1.5) {
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a));
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+173:
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)))
	elif b <= -1.5:
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a))
	else:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+173)
		tmp = Float64(x * Float64(Float64(Float64(b / y) / Float64(-a)) - Float64(-1.0 / Float64(y * a))));
	elseif (b <= -1.5)
		tmp = Float64(Float64(a * Float64(Float64(y * Float64(x / y)) - Float64(x * b))) / Float64(y * Float64(a * a)));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+173)
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	elseif (b <= -1.5)
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a));
	else
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+173], N[(x * N[(N[(N[(b / y), $MachinePrecision] / (-a)), $MachinePrecision] - N[(-1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5], N[(N[(a * N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000009e173

   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 88.0%

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

      4. associate-/l* 88.0%

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

      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 76.0%

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

      8. *-commutative 76.0%

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

      9. exp-to-pow 76.0%

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

      10. sub-neg 76.0%

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

      11. metadata-eval 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around 0 88.0%

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

   6. Taylor expanded in y around 0 100.0%

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

   7. Taylor expanded in b around 0 50.3%

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

   8. Taylor expanded in x around -inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. *-commutative 54.2%

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

      3. distribute-rgt-neg-in 54.2%

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

      4. sub-neg 54.2%

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

      5. *-commutative 54.2%

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

      6. associate-/r* 69.4%

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

      7. distribute-neg-frac 69.4%

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

      8. metadata-eval 69.4%

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

   10. Simplified 69.4%

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

   if -1.25000000000000009e173 < b < -1.5

   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 81.6%

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

      4. associate-/l* 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 63.2%

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

      8. *-commutative 63.2%

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

      9. exp-to-pow 63.2%

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

      10. sub-neg 63.2%

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

      11. metadata-eval 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in t around 0 66.1%

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

   6. Taylor expanded in y around 0 66.3%

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

   7. Taylor expanded in b around 0 34.3%

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

      1. +-commutative 34.3%

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

      2. *-un-lft-identity 34.3%

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

      3. frac-times 31.8%

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

      4. associate-*l/ 31.8%

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

      5. *-un-lft-identity 31.8%

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

      6. associate-*r/ 31.8%

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

      7. frac-add 43.4%

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

   9. Applied egg-rr 43.4%

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

       1. +-commutative 43.4%

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

       2. *-commutative 43.4%

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

       3. associate-*l* 46.0%

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

       4. distribute-lft-out 46.0%

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

       5. mul-1-neg 46.0%

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

       6. distribute-rgt-neg-in 46.0%

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

       7. associate-*r* 48.1%

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

   11. Simplified 48.1%

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

   if -1.5 < b

   1. Initial program 95.4%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 79.1%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in y around 0 53.7%

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

   7. Taylor expanded in b around 0 48.9%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(\frac{\frac{b}{y}}{-a} - \frac{-1}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.5:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.0% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(\frac{\frac{b}{y}}{-a} - \frac{-1}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{+21}:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + \left(y \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+173)
   (* x (- (/ (/ b y) (- a)) (/ -1.0 (* y a))))
   (if (<= b -1.12e+21)
     (/ (* a (- (* y (/ x y)) (* x b))) (* y (* a a)))
     (/ x (* a (+ y (* b (+ y (* (* y b) 0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+173) {
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	} else if (b <= -1.12e+21) {
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a));
	} else {
		tmp = x / (a * (y + (b * (y + ((y * 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 <= (-1.25d+173)) then
        tmp = x * (((b / y) / -a) - ((-1.0d0) / (y * a)))
    else if (b <= (-1.12d+21)) then
        tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a))
    else
        tmp = x / (a * (y + (b * (y + ((y * 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 <= -1.25e+173) {
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	} else if (b <= -1.12e+21) {
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a));
	} else {
		tmp = x / (a * (y + (b * (y + ((y * b) * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+173:
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)))
	elif b <= -1.12e+21:
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a))
	else:
		tmp = x / (a * (y + (b * (y + ((y * b) * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+173)
		tmp = Float64(x * Float64(Float64(Float64(b / y) / Float64(-a)) - Float64(-1.0 / Float64(y * a))));
	elseif (b <= -1.12e+21)
		tmp = Float64(Float64(a * Float64(Float64(y * Float64(x / y)) - Float64(x * b))) / Float64(y * Float64(a * a)));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(Float64(y * b) * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+173)
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	elseif (b <= -1.12e+21)
		tmp = (a * ((y * (x / y)) - (x * b))) / (y * (a * a));
	else
		tmp = x / (a * (y + (b * (y + ((y * b) * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+173], N[(x * N[(N[(N[(b / y), $MachinePrecision] / (-a)), $MachinePrecision] - N[(-1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.12e+21], N[(N[(a * N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(N[(y * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000009e173

   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 88.0%

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

      4. associate-/l* 88.0%

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

      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 76.0%

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

      8. *-commutative 76.0%

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

      9. exp-to-pow 76.0%

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

      10. sub-neg 76.0%

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

      11. metadata-eval 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around 0 88.0%

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

   6. Taylor expanded in y around 0 100.0%

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

   7. Taylor expanded in b around 0 50.3%

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

   8. Taylor expanded in x around -inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. *-commutative 54.2%

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

      3. distribute-rgt-neg-in 54.2%

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

      4. sub-neg 54.2%

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

      5. *-commutative 54.2%

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

      6. associate-/r* 69.4%

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

      7. distribute-neg-frac 69.4%

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

      8. metadata-eval 69.4%

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

   10. Simplified 69.4%

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

   if -1.25000000000000009e173 < b < -1.12e21

   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 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* 84.4%

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

      5. *-commutative 84.4%

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

      6. exp-to-pow 84.4%

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

      7. exp-diff 62.5%

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

      8. *-commutative 62.5%

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

      9. exp-to-pow 62.5%

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

      10. sub-neg 62.5%

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

      11. metadata-eval 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in t around 0 66.0%

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

   6. Taylor expanded in y around 0 66.2%

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

   7. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. *-un-lft-identity 37.1%

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

      3. frac-times 34.1%

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

      4. associate-*l/ 34.1%

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

      5. *-un-lft-identity 34.1%

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

      6. associate-*r/ 34.1%

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

      7. frac-add 48.0%

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

   9. Applied egg-rr 48.0%

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

       1. +-commutative 48.0%

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

       2. *-commutative 48.0%

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

       3. associate-*l* 51.1%

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

       4. distribute-lft-out 51.1%

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

       5. mul-1-neg 51.1%

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

       6. distribute-rgt-neg-in 51.1%

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

       7. associate-*r* 53.6%

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

   11. Simplified 53.6%

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

   if -1.12e21 < b

   1. Initial program 95.6%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 78.7%

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

      4. associate-/l* 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. exp-diff 70.7%

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

      8. *-commutative 70.7%

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

      9. exp-to-pow 71.6%

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

      10. sub-neg 71.6%

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

      11. metadata-eval 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in y around 0 54.1%

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

   7. Taylor expanded in b around 0 42.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(\frac{\frac{b}{y}}{-a} - \frac{-1}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{+21}:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + \left(y \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.6% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(\frac{\frac{b}{y}}{-a} - \frac{-1}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + \left(y \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+115)
   (* x (- (/ (/ b y) (- a)) (/ -1.0 (* y a))))
   (/ x (* a (+ y (* b (+ y (* (* y b) 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+115) {
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + ((y * 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 <= (-3.5d+115)) then
        tmp = x * (((b / y) / -a) - ((-1.0d0) / (y * a)))
    else
        tmp = x / (a * (y + (b * (y + ((y * 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 <= -3.5e+115) {
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + ((y * b) * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+115:
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)))
	else:
		tmp = x / (a * (y + (b * (y + ((y * b) * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+115)
		tmp = Float64(x * Float64(Float64(Float64(b / y) / Float64(-a)) - Float64(-1.0 / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(Float64(y * b) * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+115)
		tmp = x * (((b / y) / -a) - (-1.0 / (y * a)));
	else
		tmp = x / (a * (y + (b * (y + ((y * b) * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+115], N[(x * N[(N[(N[(b / y), $MachinePrecision] / (-a)), $MachinePrecision] - N[(-1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(N[(y * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.50000000000000005e115

   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 91.9%

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

      4. associate-/l* 91.9%

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

      5. *-commutative 91.9%

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

      6. exp-to-pow 91.9%

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

      7. exp-diff 70.3%

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

      8. *-commutative 70.3%

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

      9. exp-to-pow 70.3%

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

      10. sub-neg 70.3%

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

      11. metadata-eval 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in t around 0 81.2%

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

   6. Taylor expanded in y around 0 89.4%

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

   7. Taylor expanded in b around 0 53.5%

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

   8. Taylor expanded in x around -inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. *-commutative 51.0%

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

      3. distribute-rgt-neg-in 51.0%

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

      4. sub-neg 51.0%

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

      5. *-commutative 51.0%

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

      6. associate-/r* 61.3%

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

      7. distribute-neg-frac 61.3%

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

      8. metadata-eval 61.3%

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

   10. Simplified 61.3%

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

   if -3.50000000000000005e115 < b

   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* 99.0%

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

      2. associate--l+ 99.0%

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

      3. exp-sum 78.4%

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

      4. associate-/l* 76.6%

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

      5. *-commutative 76.6%

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

      6. exp-to-pow 76.6%

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

      7. exp-diff 70.2%

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

      8. *-commutative 70.2%

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

      9. exp-to-pow 71.0%

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

      10. sub-neg 71.0%

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

      11. metadata-eval 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in t around 0 66.7%

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

   6. Taylor expanded in y around 0 55.1%

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

   7. Taylor expanded in b around 0 41.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(\frac{\frac{b}{y}}{-a} - \frac{-1}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + \left(y \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.1% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.74:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(\left(--1\right) - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.74) (/ (* (/ x a) (- (- -1.0) b)) y) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.74) {
		tmp = ((x / a) * (-(-1.0) - b)) / y;
	} else {
		tmp = x / (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 <= (-0.74d0)) then
        tmp = ((x / a) * (-(-1.0d0) - b)) / y
    else
        tmp = x / (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 <= -0.74) {
		tmp = ((x / a) * (-(-1.0) - b)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.74:
		tmp = ((x / a) * (-(-1.0) - b)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.74)
		tmp = Float64(Float64(Float64(x / a) * Float64(Float64(-(-1.0)) - b)) / y);
	else
		tmp = Float64(x / 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 <= -0.74)
		tmp = ((x / a) * (-(-1.0) - b)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.74], N[(N[(N[(x / a), $MachinePrecision] * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.73999999999999999

   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 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* 84.1%

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

      5. *-commutative 84.1%

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

      6. exp-to-pow 84.1%

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

      7. exp-diff 68.3%

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

      8. *-commutative 68.3%

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

      9. exp-to-pow 68.3%

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

      10. sub-neg 68.3%

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

      11. metadata-eval 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around 0 74.8%

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

   6. Taylor expanded in y around 0 79.7%

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

   7. Taylor expanded in b around 0 40.7%

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

   8. Taylor expanded in y around -inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. distribute-neg-frac2 50.9%

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

      3. +-commutative 50.9%

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

      4. associate-/l* 47.9%

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

      5. distribute-rgt-out 47.9%

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

   10. Simplified 47.9%

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

   if -0.73999999999999999 < b

   1. Initial program 95.4%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 79.1%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in y around 0 53.7%

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

   7. Taylor expanded in b around 0 37.9%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.74:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(\left(--1\right) - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.4% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.85:\\ \;\;\;\;\frac{b \cdot \frac{x}{-y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.85) (/ (* b (/ x (- y))) a) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.85) {
		tmp = (b * (x / -y)) / a;
	} else {
		tmp = x / (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 <= (-0.85d0)) then
        tmp = (b * (x / -y)) / a
    else
        tmp = x / (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 <= -0.85) {
		tmp = (b * (x / -y)) / a;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.85:
		tmp = (b * (x / -y)) / a
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.85)
		tmp = Float64(Float64(b * Float64(x / Float64(-y))) / a);
	else
		tmp = Float64(x / 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 <= -0.85)
		tmp = (b * (x / -y)) / a;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.85], N[(N[(b * N[(x / (-y)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.849999999999999978

   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 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* 84.1%

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

      5. *-commutative 84.1%

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

      6. exp-to-pow 84.1%

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

      7. exp-diff 68.3%

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

      8. *-commutative 68.3%

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

      9. exp-to-pow 68.3%

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

      10. sub-neg 68.3%

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

      11. metadata-eval 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in t around 0 74.8%

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

   6. Taylor expanded in y around 0 79.7%

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

   7. Taylor expanded in b around 0 40.7%

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

   8. Taylor expanded in b around inf 40.7%

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

      1. times-frac 42.1%

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

      2. associate-*l/ 42.2%

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

      3. associate-*r/ 36.4%

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

      4. associate-*r* 36.4%

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

      5. associate-*r/ 42.2%

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

      6. neg-mul-1 42.2%

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

   10. Simplified 42.2%

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

   if -0.849999999999999978 < b

   1. Initial program 95.4%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 79.1%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in y around 0 53.7%

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

   7. Taylor expanded in b around 0 37.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.85:\\ \;\;\;\;\frac{b \cdot \frac{x}{-y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.5% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.1e-5) (* b (/ x (* y (- a)))) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.1e-5) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.1d-5)) then
        tmp = b * (x / (y * -a))
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.1e-5) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.1e-5:
		tmp = b * (x / (y * -a))
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.1e-5)
		tmp = Float64(b * Float64(x / Float64(y * Float64(-a))));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.1e-5)
		tmp = b * (x / (y * -a));
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.1e-5], N[(b * N[(x / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.09999999999999996e-5

   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 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* 84.4%

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

      5. *-commutative 84.4%

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

      6. exp-to-pow 84.4%

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

      7. exp-diff 68.8%

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

      8. *-commutative 68.8%

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

      9. exp-to-pow 68.8%

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

      10. sub-neg 68.8%

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

      11. metadata-eval 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in t around 0 75.2%

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

   6. Taylor expanded in y around 0 80.0%

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

   7. Taylor expanded in b around 0 41.6%

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

   8. Taylor expanded in b around inf 41.6%

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

      1. associate-*r/ 41.6%

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

      2. mul-1-neg 41.6%

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

      3. distribute-rgt-neg-in 41.6%

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

      4. associate-*r/ 38.8%

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

   10. Simplified 38.8%

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

   if -5.09999999999999996e-5 < b

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 0 72.0%

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

   4. Taylor expanded in b around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. exp-to-pow 61.3%

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

      3. sub-neg 61.3%

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

      4. metadata-eval 61.3%

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

      5. associate-*r/ 59.2%

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

      6. +-commutative 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in t around 0 34.6%

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

   8. Taylor expanded in a around 0 34.2%

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

      1. associate-/l/ 34.6%

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

   10. Simplified 34.6%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.1% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+136) (/ (* b (/ x (- y))) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+136) {
		tmp = (b * (x / -y)) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+136)) then
        tmp = (b * (x / -y)) / a
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+136) {
		tmp = (b * (x / -y)) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+136:
		tmp = (b * (x / -y)) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+136)
		tmp = Float64(Float64(b * Float64(x / Float64(-y))) / a);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+136)
		tmp = (b * (x / -y)) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+136], N[(N[(b * N[(x / (-y)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e136

   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 90.9%

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

      4. associate-/l* 90.9%

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

      5. *-commutative 90.9%

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

      6. exp-to-pow 90.9%

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

      7. exp-diff 69.7%

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

      8. *-commutative 69.7%

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

      9. exp-to-pow 69.7%

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

      10. sub-neg 69.7%

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

      11. metadata-eval 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in t around 0 81.9%

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

   6. Taylor expanded in y around 0 91.1%

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

   7. Taylor expanded in b around 0 53.7%

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

   8. Taylor expanded in b around inf 53.7%

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

      1. times-frac 53.8%

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

      2. associate-*l/ 59.5%

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

      3. associate-*r/ 48.4%

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

      4. associate-*r* 48.4%

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

      5. associate-*r/ 59.5%

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

      6. neg-mul-1 59.5%

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

   10. Simplified 59.5%

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

   if -1.15e136 < b

   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* 99.0%

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

      2. associate--l+ 99.0%

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

      3. exp-sum 78.8%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 70.3%

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

      8. *-commutative 70.3%

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

      9. exp-to-pow 71.1%

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

      10. sub-neg 71.1%

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

      11. metadata-eval 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in t around 0 66.9%

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

   6. Taylor expanded in y around 0 55.5%

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

   7. Taylor expanded in b around 0 33.4%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.3% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4e-101) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4e-101) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 4d-101) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4e-101) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4e-101:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4e-101)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4e-101)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4e-101], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.00000000000000021e-101

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. mul-1-neg 87.1%

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

      3. unsub-neg 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in b around 0 73.0%

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

      1. exp-diff 72.9%

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

      2. *-commutative 72.9%

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

      3. exp-to-pow 72.9%

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

      4. rem-exp-log 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in y around 0 42.9%

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

   if 4.00000000000000021e-101 < a

   1. Initial program 95.3%

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

      1. associate-/l* 99.0%

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

      2. associate--l+ 99.0%

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

      3. exp-sum 81.5%

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

      4. associate-/l* 79.2%

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

      5. *-commutative 79.2%

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

      6. exp-to-pow 79.2%

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

      7. exp-diff 67.4%

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

      8. *-commutative 67.4%

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

      9. exp-to-pow 68.1%

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

      10. sub-neg 68.1%

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

      11. metadata-eval 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in t around 0 64.4%

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

   6. Taylor expanded in y around 0 56.6%

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

   7. Taylor expanded in b around 0 31.7%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{-101}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.9% 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 96.6%

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

   1. associate-/l* 99.1%

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

   2. associate--l+ 99.1%

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

   3. exp-sum 80.3%

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

   4. associate-/l* 78.8%

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

   5. *-commutative 78.8%

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

   6. exp-to-pow 78.8%

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

   7. exp-diff 70.2%

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

   8. *-commutative 70.2%

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

   9. exp-to-pow 70.9%

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

   10. sub-neg 70.9%

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

   11. metadata-eval 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in t around 0 68.8%

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

6. Taylor expanded in y around 0 60.1%

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

7. Taylor expanded in b around 0 32.9%

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

8. Final simplification 32.9%

   \[\leadsto \frac{x}{y \cdot a} \]
9. Add Preprocessing

Developer target: 71.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024082 
(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))