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

Percentage Accurate: 98.3% → 98.3%

Time: 19.7s

Alternatives: 24

Speedup: 1.0×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+67)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (if (<= (+ t -1.0) 4e+105)
     (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
     (* x (/ (pow a (+ t -1.0)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+67) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else if ((t + -1.0) <= 4e+105) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-5d+67)) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else if ((t + (-1.0d0)) <= 4d+105) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+67) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else if ((t + -1.0) <= 4e+105) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+67:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	elif (t + -1.0) <= 4e+105:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+67)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	elseif (Float64(t + -1.0) <= 4e+105)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+67)
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	elseif ((t + -1.0) <= 4e+105)
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+67], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+105], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -4.99999999999999976e67

   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 95.7%

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

   if -4.99999999999999976e67 < (-.f64 t #s(literal 1 binary64)) < 3.9999999999999998e105

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. mul-1-neg 95.6%

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

      3. unsub-neg 95.6%

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

   5. Simplified 95.6%

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

   if 3.9999999999999998e105 < (-.f64 t #s(literal 1 binary64))

   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. exp-diff 92.7%

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

      3. associate-/l/ 92.7%

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

      4. exp-sum 75.6%

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

      5. associate-/l* 75.6%

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

      6. *-commutative 75.6%

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

      7. exp-to-pow 75.6%

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

      8. *-commutative 75.6%

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

      9. exp-to-pow 75.6%

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

      10. sub-neg 75.6%

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

      11. metadata-eval 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. exp-to-pow 92.7%

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

      2. sub-neg 92.7%

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

      3. metadata-eval 92.7%

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

      4. associate-/r* 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in b around 0 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+55)
   (* x (/ (pow a (+ t -1.0)) y))
   (if (<= (+ t -1.0) 2e+79)
     (* (/ (pow z y) a) (/ x (* y (exp b))))
     (/ (* x (/ (pow a t) a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else if ((t + -1.0) <= 2e+79) {
		tmp = (pow(z, y) / a) * (x / (y * exp(b)));
	} else {
		tmp = (x * (pow(a, t) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-5d+55)) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else if ((t + (-1.0d0)) <= 2d+79) then
        tmp = ((z ** y) / a) * (x / (y * exp(b)))
    else
        tmp = (x * ((a ** t) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else if ((t + -1.0) <= 2e+79) {
		tmp = (Math.pow(z, y) / a) * (x / (y * Math.exp(b)));
	} else {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+55:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	elif (t + -1.0) <= 2e+79:
		tmp = (math.pow(z, y) / a) * (x / (y * math.exp(b)))
	else:
		tmp = (x * (math.pow(a, t) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+55)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	elseif (Float64(t + -1.0) <= 2e+79)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+55)
		tmp = x * ((a ^ (t + -1.0)) / y);
	elseif ((t + -1.0) <= 2e+79)
		tmp = ((z ^ y) / a) * (x / (y * exp(b)));
	else
		tmp = (x * ((a ^ t) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+55], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+79], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -5.00000000000000046e55

   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. exp-diff 82.4%

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

      3. associate-/l/ 82.4%

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

      4. exp-sum 70.6%

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

      5. associate-/l* 70.6%

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

      6. *-commutative 70.6%

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

      7. exp-to-pow 70.6%

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

      8. *-commutative 70.6%

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

      9. exp-to-pow 70.6%

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

      10. sub-neg 70.6%

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

      11. metadata-eval 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 82.4%

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

      1. exp-to-pow 82.4%

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

      2. sub-neg 82.4%

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

      3. metadata-eval 82.4%

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

      4. associate-/r* 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in b around 0 92.3%

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

   10. Simplified 92.3%

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

   if -5.00000000000000046e55 < (-.f64 t #s(literal 1 binary64)) < 1.99999999999999993e79

   1. Initial program 97.3%

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

      1. associate-/l* 97.9%

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

      2. exp-diff 82.3%

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

      3. associate-/l/ 82.3%

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

      4. exp-sum 78.5%

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

      5. associate-/l* 76.7%

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

      6. *-commutative 76.7%

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

      7. exp-to-pow 76.7%

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

      8. *-commutative 76.7%

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

      9. exp-to-pow 77.4%

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

      10. sub-neg 77.4%

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

      11. metadata-eval 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in t around 0 82.5%

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

      1. *-commutative 82.5%

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

      2. times-frac 82.5%

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

   7. Simplified 82.5%

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

   if 1.99999999999999993e79 < (-.f64 t #s(literal 1 binary64))

   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 95.6%

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

      1. div-exp 89.0%

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

      2. exp-to-pow 89.0%

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

      3. sub-neg 89.0%

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

      4. metadata-eval 89.0%

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

   5. Simplified 89.0%

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

      1. unpow-prod-up 89.0%

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

      2. unpow-1 89.0%

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

   7. Applied egg-rr 89.0%

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

      1. associate-*r/ 89.0%

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

      2. *-rgt-identity 89.0%

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

   9. Simplified 89.0%

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

   10. Taylor expanded in b around 0 93.4%

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

       1. associate-/l* 93.4%

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

   12. Simplified 93.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16} \lor \neg \left(y \leq 2.6 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e+16) (not (<= y 2.6e+95)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+16) || !(y <= 2.6e+95)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8d+16)) .or. (.not. (y <= 2.6d+95))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+16) || !(y <= 2.6e+95)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e+16) or not (y <= 2.6e+95):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e+16) || !(y <= 2.6e+95))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8e+16) || ~((y <= 2.6e+95)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e+16], N[Not[LessEqual[y, 2.6e+95]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e16 or 2.5999999999999999e95 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.2%

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

      1. exp-sum 68.4%

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

      2. *-commutative 68.4%

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

      3. exp-to-pow 68.4%

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

      4. exp-to-pow 68.4%

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

      5. sub-neg 68.4%

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

      6. metadata-eval 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in t around 0 81.5%

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

   if -8e16 < y < 2.5999999999999999e95

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 95.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16} \lor \neg \left(y \leq 2.6 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+16} \lor \neg \left(y \leq 3.9 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e+16) (not (<= y 3.9e+87)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (/ (/ (pow a t) a) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+16) || !(y <= 3.9e+87)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * ((pow(a, t) / a) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.5d+16)) .or. (.not. (y <= 3.9d+87))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * (((a ** t) / a) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+16) || !(y <= 3.9e+87)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * ((Math.pow(a, t) / a) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.5e+16) or not (y <= 3.9e+87):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * ((math.pow(a, t) / a) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.5e+16) || !(y <= 3.9e+87))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * Float64(Float64((a ^ t) / a) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.5e+16) || ~((y <= 3.9e+87)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * (((a ^ t) / a) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.5e+16], N[Not[LessEqual[y, 3.9e+87]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e16 or 3.9000000000000002e87 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 92.3%

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

      1. exp-sum 67.8%

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

      2. *-commutative 67.8%

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

      3. exp-to-pow 67.8%

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

      4. exp-to-pow 67.8%

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

      5. sub-neg 67.8%

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

      6. metadata-eval 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around 0 80.7%

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

   if -5.5e16 < y < 3.9000000000000002e87

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 95.3%

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

      1. div-exp 90.2%

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

      2. exp-to-pow 91.0%

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

      3. sub-neg 91.0%

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

      4. metadata-eval 91.0%

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

   5. Simplified 91.0%

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

      1. unpow-prod-up 91.1%

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

      2. unpow-1 91.1%

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

   7. Applied egg-rr 91.1%

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

      1. associate-*r/ 91.1%

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

      2. *-rgt-identity 91.1%

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

   9. Simplified 91.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+16} \lor \neg \left(y \leq 3.9 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+16} \lor \neg \left(y \leq 1.15 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+16) (not (<= y 1.15e+92)))
   (/ (/ (* x (pow z y)) a) y)
   (* x (/ (/ (pow a (+ t -1.0)) y) (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+16) || !(y <= 1.15e+92)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = x * ((pow(a, (t + -1.0)) / y) / exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.6d+16)) .or. (.not. (y <= 1.15d+92))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = x * (((a ** (t + (-1.0d0))) / y) / exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+16) || !(y <= 1.15e+92)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = x * ((Math.pow(a, (t + -1.0)) / y) / Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.6e+16) or not (y <= 1.15e+92):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = x * ((math.pow(a, (t + -1.0)) / y) / math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e+16) || !(y <= 1.15e+92))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / y) / exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.6e+16) || ~((y <= 1.15e+92)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = x * (((a ^ (t + -1.0)) / y) / exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+16], N[Not[LessEqual[y, 1.15e+92]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e16 or 1.14999999999999999e92 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 92.3%

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

      1. exp-sum 67.8%

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

      2. *-commutative 67.8%

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

      3. exp-to-pow 67.8%

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

      4. exp-to-pow 67.8%

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

      5. sub-neg 67.8%

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

      6. metadata-eval 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around 0 80.7%

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

   if -3.6e16 < y < 1.14999999999999999e92

   1. Initial program 97.2%

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

      1. associate-/l* 97.8%

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

      2. exp-diff 89.4%

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

      3. associate-/l/ 89.4%

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

      4. exp-sum 86.8%

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

      5. associate-/l* 86.8%

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

      6. *-commutative 86.8%

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

      7. exp-to-pow 86.8%

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

      8. *-commutative 86.8%

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

      9. exp-to-pow 87.6%

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

      10. sub-neg 87.6%

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

      11. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 90.8%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

      4. associate-/r* 89.0%

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

   7. Simplified 89.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+16} \lor \neg \left(y \leq 1.15 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+62} \lor \neg \left(t + -1 \leq 4 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -2e+62) (not (<= (+ t -1.0) 4e+105)))
   (* x (/ (pow a (+ t -1.0)) y))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+62) || !((t + -1.0) <= 4e+105)) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-2d+62)) .or. (.not. ((t + (-1.0d0)) <= 4d+105))) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+62) || !((t + -1.0) <= 4e+105)) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -2e+62) or not ((t + -1.0) <= 4e+105):
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -2e+62) || !(Float64(t + -1.0) <= 4e+105))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -2e+62) || ~(((t + -1.0) <= 4e+105)))
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+62], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+105]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -2.00000000000000007e62 or 3.9999999999999998e105 < (-.f64 t #s(literal 1 binary64))

   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. exp-diff 87.8%

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

      3. associate-/l/ 87.8%

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

      4. exp-sum 73.3%

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

      5. associate-/l* 73.3%

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

      6. *-commutative 73.3%

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

      7. exp-to-pow 73.3%

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

      8. *-commutative 73.3%

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

      9. exp-to-pow 73.3%

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

      10. sub-neg 73.3%

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

      11. metadata-eval 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around 0 87.8%

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

      1. exp-to-pow 87.8%

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

      2. sub-neg 87.8%

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

      3. metadata-eval 87.8%

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

      4. associate-/r* 87.8%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in b around 0 95.6%

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

   10. Simplified 95.6%

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

   if -2.00000000000000007e62 < (-.f64 t #s(literal 1 binary64)) < 3.9999999999999998e105

   1. Initial program 97.4%

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

      1. associate-/l* 98.0%

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

      2. exp-diff 81.7%

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

      3. associate-/l/ 81.7%

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

      4. exp-sum 76.9%

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

      5. associate-/l* 75.1%

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

      6. *-commutative 75.1%

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

      7. exp-to-pow 75.1%

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

      8. *-commutative 75.1%

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

      9. exp-to-pow 75.8%

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

      10. sub-neg 75.8%

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

      11. metadata-eval 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in y around 0 67.3%

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

      1. exp-to-pow 68.1%

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

      2. sub-neg 68.1%

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

      3. metadata-eval 68.1%

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

      4. associate-/r* 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in t around 0 71.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+62} \lor \neg \left(t + -1 \leq 4 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.0% 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 98.3%

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

   1. associate-/l* 98.7%

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

   2. exp-diff 83.9%

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

   3. associate-/l/ 83.9%

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

   4. exp-sum 75.7%

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

   5. associate-/l* 74.5%

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

   6. *-commutative 74.5%

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

   7. exp-to-pow 74.5%

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

   8. *-commutative 74.5%

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

   9. exp-to-pow 75.0%

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

   10. sub-neg 75.0%

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

   11. metadata-eval 75.0%

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

3. Simplified 75.0%

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

5. Taylor expanded in y around 0 74.5%

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

   1. exp-to-pow 75.0%

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

   2. sub-neg 75.0%

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

   3. metadata-eval 75.0%

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

   4. associate-/r* 72.3%

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

7. Simplified 72.3%

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

8. Taylor expanded in t around 0 62.3%

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

Alternative 9: 49.6% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-184}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.4e+128)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b -5.2e+90)
     (/
      x
      (*
       a
       (+ y (* b (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5))))))))
     (if (<= b -1.1e-143)
       (* x (/ 1.0 (* y a)))
       (if (<= b 2e-184)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (/
          (/
           x
           (+
            a
            (* b (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
          y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.4e+128) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= -5.2e+90) {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	} else if (b <= -1.1e-143) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 2e-184) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.4d+128)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= (-5.2d+90)) then
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    else if (b <= (-1.1d-143)) then
        tmp = x * (1.0d0 / (y * a))
    else if (b <= 2d-184) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.4e+128) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= -5.2e+90) {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	} else if (b <= -1.1e-143) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 2e-184) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.4e+128:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= -5.2e+90:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	elif b <= -1.1e-143:
		tmp = x * (1.0 / (y * a))
	elif b <= 2e-184:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.4e+128)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= -5.2e+90)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	elseif (b <= -1.1e-143)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 2e-184)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.4e+128)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= -5.2e+90)
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	elseif (b <= -1.1e-143)
		tmp = x * (1.0 / (y * a));
	elseif (b <= 2e-184)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.4e+128], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -5.2e+90], 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], If[LessEqual[b, -1.1e-143], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-184], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.4000000000000002e128

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 70.0%

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

   8. Taylor expanded in x around 0 83.8%

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

   if -7.4000000000000002e128 < b < -5.1999999999999997e90

   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. exp-diff 27.3%

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

      3. associate-/l/ 27.3%

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

      4. exp-sum 27.3%

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

      5. associate-/l* 27.3%

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

      6. *-commutative 27.3%

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

      7. exp-to-pow 27.3%

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

      8. *-commutative 27.3%

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

      9. exp-to-pow 27.3%

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

      10. sub-neg 27.3%

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

      11. metadata-eval 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in y around 0 36.8%

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

      1. exp-to-pow 36.8%

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

      2. sub-neg 36.8%

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

      3. metadata-eval 36.8%

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

      4. associate-/r* 36.8%

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

   7. Simplified 36.8%

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

   8. Taylor expanded in t around 0 37.4%

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

   9. Taylor expanded in b around 0 64.2%

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

   if -5.1999999999999997e90 < b < -1.09999999999999995e-143

   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* 97.4%

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

      2. exp-diff 86.7%

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

      3. associate-/l/ 86.7%

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

      4. exp-sum 80.4%

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

      5. associate-/l* 78.2%

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

      6. *-commutative 78.2%

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

      7. exp-to-pow 78.2%

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

      8. *-commutative 78.2%

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

      9. exp-to-pow 78.6%

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

      10. sub-neg 78.6%

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

      11. metadata-eval 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around 0 70.4%

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

      1. exp-to-pow 70.8%

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

      2. sub-neg 70.8%

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

      3. metadata-eval 70.8%

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

      4. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in t around 0 52.8%

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

   9. Taylor expanded in b around 0 32.2%

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

       1. div-inv 34.3%

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

   11. Applied egg-rr 34.3%

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

   if -1.09999999999999995e-143 < b < 2.0000000000000001e-184

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. div-exp 80.6%

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

      2. exp-to-pow 81.1%

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

      3. sub-neg 81.1%

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

      4. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 37.9%

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

      1. +-commutative 37.9%

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

      2. mul-1-neg 37.9%

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

      3. unsub-neg 37.9%

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

      4. associate-/l* 34.3%

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

   9. Simplified 34.3%

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

   10. Taylor expanded in b around inf 51.5%

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

   if 2.0000000000000001e-184 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 77.6%

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

      3. sub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 69.3%

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

   7. Taylor expanded in b around 0 63.8%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-184}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-181}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+128)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b -3.5e+91)
     (/
      x
      (*
       a
       (+ y (* b (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5))))))))
     (if (<= b -1.2e-142)
       (* x (/ 1.0 (* y a)))
       (if (<= b 2.4e-181)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+128) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= -3.5e+91) {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	} else if (b <= -1.2e-142) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 2.4e-181) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (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 (b <= (-3.5d+128)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= (-3.5d+91)) then
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    else if (b <= (-1.2d-142)) then
        tmp = x * (1.0d0 / (y * a))
    else if (b <= 2.4d-181) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (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 (b <= -3.5e+128) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= -3.5e+91) {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	} else if (b <= -1.2e-142) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 2.4e-181) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+128:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= -3.5e+91:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	elif b <= -1.2e-142:
		tmp = x * (1.0 / (y * a))
	elif b <= 2.4e-181:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+128)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= -3.5e+91)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	elseif (b <= -1.2e-142)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 2.4e-181)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+128)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= -3.5e+91)
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	elseif (b <= -1.2e-142)
		tmp = x * (1.0 / (y * a));
	elseif (b <= 2.4e-181)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+128], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.5e+91], 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], If[LessEqual[b, -1.2e-142], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-181], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.49999999999999969e128

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 70.0%

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

   8. Taylor expanded in x around 0 83.8%

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

   if -3.49999999999999969e128 < b < -3.50000000000000001e91

   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. exp-diff 27.3%

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

      3. associate-/l/ 27.3%

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

      4. exp-sum 27.3%

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

      5. associate-/l* 27.3%

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

      6. *-commutative 27.3%

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

      7. exp-to-pow 27.3%

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

      8. *-commutative 27.3%

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

      9. exp-to-pow 27.3%

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

      10. sub-neg 27.3%

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

      11. metadata-eval 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in y around 0 36.8%

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

      1. exp-to-pow 36.8%

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

      2. sub-neg 36.8%

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

      3. metadata-eval 36.8%

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

      4. associate-/r* 36.8%

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

   7. Simplified 36.8%

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

   8. Taylor expanded in t around 0 37.4%

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

   9. Taylor expanded in b around 0 64.2%

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

   if -3.50000000000000001e91 < b < -1.19999999999999994e-142

   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* 97.4%

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

      2. exp-diff 86.7%

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

      3. associate-/l/ 86.7%

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

      4. exp-sum 80.4%

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

      5. associate-/l* 78.2%

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

      6. *-commutative 78.2%

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

      7. exp-to-pow 78.2%

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

      8. *-commutative 78.2%

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

      9. exp-to-pow 78.6%

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

      10. sub-neg 78.6%

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

      11. metadata-eval 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around 0 70.4%

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

      1. exp-to-pow 70.8%

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

      2. sub-neg 70.8%

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

      3. metadata-eval 70.8%

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

      4. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in t around 0 52.8%

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

   9. Taylor expanded in b around 0 32.2%

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

       1. div-inv 34.3%

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

   11. Applied egg-rr 34.3%

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

   if -1.19999999999999994e-142 < b < 2.4000000000000001e-181

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. div-exp 80.6%

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

      2. exp-to-pow 81.1%

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

      3. sub-neg 81.1%

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

      4. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 37.9%

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

      1. +-commutative 37.9%

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

      2. mul-1-neg 37.9%

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

      3. unsub-neg 37.9%

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

      4. associate-/l* 34.3%

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

   9. Simplified 34.3%

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

   10. Taylor expanded in b around inf 51.5%

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

   if 2.4000000000000001e-181 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 77.6%

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

      3. sub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 69.3%

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

   7. Taylor expanded in b around 0 60.3%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-181}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)))
   (if (<= b -3.5e+128)
     t_1
     (if (<= b -1.35e+111)
       (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))
       (if (<= b -1.35e-100)
         t_1
         (if (<= b 4.5e-181)
           (/ (* b (- (/ x (* a b)) (/ x a))) y)
           (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	double tmp;
	if (b <= -3.5e+128) {
		tmp = t_1;
	} else if (b <= -1.35e+111) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= -1.35e-100) {
		tmp = t_1;
	} else if (b <= 4.5e-181) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    if (b <= (-3.5d+128)) then
        tmp = t_1
    else if (b <= (-1.35d+111)) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    else if (b <= (-1.35d-100)) then
        tmp = t_1
    else if (b <= 4.5d-181) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (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 t_1 = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	double tmp;
	if (b <= -3.5e+128) {
		tmp = t_1;
	} else if (b <= -1.35e+111) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= -1.35e-100) {
		tmp = t_1;
	} else if (b <= 4.5e-181) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	tmp = 0
	if b <= -3.5e+128:
		tmp = t_1
	elif b <= -1.35e+111:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	elif b <= -1.35e-100:
		tmp = t_1
	elif b <= 4.5e-181:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y)
	tmp = 0.0
	if (b <= -3.5e+128)
		tmp = t_1;
	elseif (b <= -1.35e+111)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	elseif (b <= -1.35e-100)
		tmp = t_1;
	elseif (b <= 4.5e-181)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	tmp = 0.0;
	if (b <= -3.5e+128)
		tmp = t_1;
	elseif (b <= -1.35e+111)
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	elseif (b <= -1.35e-100)
		tmp = t_1;
	elseif (b <= 4.5e-181)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3.5e+128], t$95$1, If[LessEqual[b, -1.35e+111], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.35e-100], t$95$1, If[LessEqual[b, 4.5e-181], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.49999999999999969e128 or -1.3499999999999999e111 < b < -1.35000000000000008e-100

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. div-exp 72.8%

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

      2. exp-to-pow 73.1%

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

      3. sub-neg 73.1%

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

      4. metadata-eval 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 74.7%

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

   7. Taylor expanded in b around 0 46.7%

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

   8. Taylor expanded in x around 0 59.6%

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

   if -3.49999999999999969e128 < b < -1.3499999999999999e111

   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. exp-diff 14.3%

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

      3. associate-/l/ 14.3%

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

      4. exp-sum 14.3%

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

      5. associate-/l* 14.3%

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

      6. *-commutative 14.3%

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

      7. exp-to-pow 14.3%

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

      8. *-commutative 14.3%

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

      9. exp-to-pow 14.3%

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

      10. sub-neg 14.3%

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

      11. metadata-eval 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in y around 0 29.0%

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

      1. exp-to-pow 29.0%

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

      2. sub-neg 29.0%

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

      3. metadata-eval 29.0%

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

      4. associate-/r* 29.0%

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

   7. Simplified 29.0%

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

   8. Taylor expanded in t around 0 29.7%

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

   9. Taylor expanded in b around 0 71.9%

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

   10. Taylor expanded in y around 0 71.9%

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

   if -1.35000000000000008e-100 < b < 4.4999999999999999e-181

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 76.2%

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

      1. div-exp 76.2%

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

      2. exp-to-pow 76.7%

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

      3. sub-neg 76.7%

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

      4. metadata-eval 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 37.2%

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

   7. Taylor expanded in b around 0 35.7%

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

      1. +-commutative 35.7%

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

      2. mul-1-neg 35.7%

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

      3. unsub-neg 35.7%

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

      4. associate-/l* 32.7%

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

   9. Simplified 32.7%

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

   10. Taylor expanded in b around inf 47.2%

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

   if 4.4999999999999999e-181 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 77.6%

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

      3. sub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 69.3%

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

   7. Taylor expanded in b around 0 60.3%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-100}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \frac{x \cdot \left(b \cdot 0.5\right) - x}{a}}{y}\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+128)
   (/ (+ (/ x a) (* b (/ (- (* x (* b 0.5)) x) a))) y)
   (if (<= b -1.46e+109)
     (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))
     (if (<= b -3.45e-158)
       (* b (- (/ x (* a (* y b))) (/ x (* y a))))
       (if (<= b 1.7e-188)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+128) {
		tmp = ((x / a) + (b * (((x * (b * 0.5)) - x) / a))) / y;
	} else if (b <= -1.46e+109) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= -3.45e-158) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if (b <= 1.7e-188) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (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 (b <= (-3.5d+128)) then
        tmp = ((x / a) + (b * (((x * (b * 0.5d0)) - x) / a))) / y
    else if (b <= (-1.46d+109)) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    else if (b <= (-3.45d-158)) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else if (b <= 1.7d-188) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (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 (b <= -3.5e+128) {
		tmp = ((x / a) + (b * (((x * (b * 0.5)) - x) / a))) / y;
	} else if (b <= -1.46e+109) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= -3.45e-158) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if (b <= 1.7e-188) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+128:
		tmp = ((x / a) + (b * (((x * (b * 0.5)) - x) / a))) / y
	elif b <= -1.46e+109:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	elif b <= -3.45e-158:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	elif b <= 1.7e-188:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+128)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(Float64(x * Float64(b * 0.5)) - x) / a))) / y);
	elseif (b <= -1.46e+109)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	elseif (b <= -3.45e-158)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	elseif (b <= 1.7e-188)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+128)
		tmp = ((x / a) + (b * (((x * (b * 0.5)) - x) / a))) / y;
	elseif (b <= -1.46e+109)
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	elseif (b <= -3.45e-158)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	elseif (b <= 1.7e-188)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+128], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(N[(x * N[(b * 0.5), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.46e+109], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.45e-158], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-188], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.49999999999999969e128

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 70.0%

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

   8. Taylor expanded in b around 0 70.0%

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

   10. Simplified 75.9%

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

   if -3.49999999999999969e128 < b < -1.46e109

   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. exp-diff 14.3%

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

      3. associate-/l/ 14.3%

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

      4. exp-sum 14.3%

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

      5. associate-/l* 14.3%

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

      6. *-commutative 14.3%

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

      7. exp-to-pow 14.3%

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

      8. *-commutative 14.3%

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

      9. exp-to-pow 14.3%

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

      10. sub-neg 14.3%

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

      11. metadata-eval 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in y around 0 29.0%

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

      1. exp-to-pow 29.0%

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

      2. sub-neg 29.0%

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

      3. metadata-eval 29.0%

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

      4. associate-/r* 29.0%

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

   7. Simplified 29.0%

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

   8. Taylor expanded in t around 0 29.7%

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

   9. Taylor expanded in b around 0 71.9%

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

   10. Taylor expanded in y around 0 71.9%

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

   if -1.46e109 < b < -3.4499999999999998e-158

   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. Add Preprocessing

   3. Taylor expanded in y around 0 73.3%

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

      1. div-exp 66.0%

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

      2. exp-to-pow 66.5%

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

      3. sub-neg 66.5%

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

      4. metadata-eval 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0 47.3%

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

   7. Taylor expanded in b around 0 29.8%

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

      1. +-commutative 29.8%

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

      2. mul-1-neg 29.8%

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

      3. unsub-neg 29.8%

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

      4. associate-/l* 29.8%

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

   9. Simplified 29.8%

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

   10. Taylor expanded in b around inf 34.3%

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

   if -3.4499999999999998e-158 < b < 1.70000000000000014e-188

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 81.0%

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

      1. div-exp 81.0%

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

      2. exp-to-pow 81.4%

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

      3. sub-neg 81.4%

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

      4. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around 0 42.3%

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

   7. Taylor expanded in b around 0 40.4%

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

      1. +-commutative 40.4%

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

      2. mul-1-neg 40.4%

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

      3. unsub-neg 40.4%

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

      4. associate-/l* 36.6%

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

   9. Simplified 36.6%

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

   10. Taylor expanded in b around inf 53.1%

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

   if 1.70000000000000014e-188 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 77.6%

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

      3. sub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 69.3%

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

   7. Taylor expanded in b around 0 60.3%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \frac{x \cdot \left(b \cdot 0.5\right) - x}{a}}{y}\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.45 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.6% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+111} \lor \neg \left(b \leq 1.95 \cdot 10^{-180}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.4e+128)
   (/ (/ (* x b) a) (- y))
   (if (or (<= b -1.2e+111) (not (<= b 1.95e-180)))
     (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))
     (/ (* b (- (/ x (* a b)) (/ x a))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.4e+128) {
		tmp = ((x * b) / a) / -y;
	} else if ((b <= -1.2e+111) || !(b <= 1.95e-180)) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.4d+128)) then
        tmp = ((x * b) / a) / -y
    else if ((b <= (-1.2d+111)) .or. (.not. (b <= 1.95d-180))) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    else
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.4e+128) {
		tmp = ((x * b) / a) / -y;
	} else if ((b <= -1.2e+111) || !(b <= 1.95e-180)) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.4e+128:
		tmp = ((x * b) / a) / -y
	elif (b <= -1.2e+111) or not (b <= 1.95e-180):
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	else:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.4e+128)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-y));
	elseif ((b <= -1.2e+111) || !(b <= 1.95e-180))
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	else
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.4e+128)
		tmp = ((x * b) / a) / -y;
	elseif ((b <= -1.2e+111) || ~((b <= 1.95e-180)))
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	else
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.4e+128], N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / (-y)), $MachinePrecision], If[Or[LessEqual[b, -1.2e+111], N[Not[LessEqual[b, 1.95e-180]], $MachinePrecision]], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.40000000000000033e128

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

   if -4.40000000000000033e128 < b < -1.20000000000000003e111 or 1.9500000000000001e-180 < b

   1. Initial program 99.2%

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

      1. associate-/l* 98.5%

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

      2. exp-diff 79.9%

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

      3. associate-/l/ 79.9%

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

      4. exp-sum 75.5%

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

      5. associate-/l* 73.7%

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

      6. *-commutative 73.7%

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

      7. exp-to-pow 73.7%

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

      8. *-commutative 73.7%

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

      9. exp-to-pow 74.3%

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

      10. sub-neg 74.3%

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

      11. metadata-eval 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around 0 73.2%

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

      1. exp-to-pow 73.8%

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

      2. sub-neg 73.8%

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

      3. metadata-eval 73.8%

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

      4. associate-/r* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in t around 0 66.0%

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

   9. Taylor expanded in b around 0 53.7%

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

   10. Taylor expanded in y around 0 56.2%

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

   if -1.20000000000000003e111 < b < 1.9500000000000001e-180

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 77.0%

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

      1. div-exp 73.3%

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

      2. exp-to-pow 73.7%

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

      3. sub-neg 73.7%

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

      4. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 44.9%

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

   7. Taylor expanded in b around 0 35.0%

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

      1. +-commutative 35.0%

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

      2. mul-1-neg 35.0%

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

      3. unsub-neg 35.0%

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

      4. associate-/l* 33.1%

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

   9. Simplified 33.1%

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

   10. Taylor expanded in b around inf 42.0%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+111} \lor \neg \left(b \leq 1.95 \cdot 10^{-180}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.8% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-172}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.5e+133)
   (/ (/ (* x b) a) (- y))
   (if (<= b -5.5e+109)
     (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))
     (if (<= b 1.65e-172)
       (/ (* b (- (/ x (* a b)) (/ x a))) y)
       (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e+133) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= -5.5e+109) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= 1.65e-172) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (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 (b <= (-4.5d+133)) then
        tmp = ((x * b) / a) / -y
    else if (b <= (-5.5d+109)) then
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    else if (b <= 1.65d-172) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (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 (b <= -4.5e+133) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= -5.5e+109) {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	} else if (b <= 1.65e-172) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.5e+133:
		tmp = ((x * b) / a) / -y
	elif b <= -5.5e+109:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	elif b <= 1.65e-172:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.5e+133)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-y));
	elseif (b <= -5.5e+109)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	elseif (b <= 1.65e-172)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.5e+133)
		tmp = ((x * b) / a) / -y;
	elseif (b <= -5.5e+109)
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	elseif (b <= 1.65e-172)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.5e+133], N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, -5.5e+109], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-172], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.49999999999999985e133

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

   if -4.49999999999999985e133 < b < -5.4999999999999998e109

   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. exp-diff 14.3%

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

      3. associate-/l/ 14.3%

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

      4. exp-sum 14.3%

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

      5. associate-/l* 14.3%

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

      6. *-commutative 14.3%

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

      7. exp-to-pow 14.3%

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

      8. *-commutative 14.3%

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

      9. exp-to-pow 14.3%

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

      10. sub-neg 14.3%

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

      11. metadata-eval 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in y around 0 29.0%

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

      1. exp-to-pow 29.0%

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

      2. sub-neg 29.0%

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

      3. metadata-eval 29.0%

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

      4. associate-/r* 29.0%

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

   7. Simplified 29.0%

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

   8. Taylor expanded in t around 0 29.7%

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

   9. Taylor expanded in b around 0 71.9%

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

   10. Taylor expanded in y around 0 71.9%

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

   if -5.4999999999999998e109 < b < 1.65e-172

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 77.0%

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

      1. div-exp 73.3%

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

      2. exp-to-pow 73.7%

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

      3. sub-neg 73.7%

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

      4. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 44.9%

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

   7. Taylor expanded in b around 0 35.0%

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

      1. +-commutative 35.0%

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

      2. mul-1-neg 35.0%

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

      3. unsub-neg 35.0%

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

      4. associate-/l* 33.1%

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

   9. Simplified 33.1%

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

   10. Taylor expanded in b around inf 42.0%

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

   if 1.65e-172 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 77.6%

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

      3. sub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 69.3%

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

   7. Taylor expanded in b around 0 60.3%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-172}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.2% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+131)
   (/ (/ (* x b) a) (- y))
   (if (<= b -9.5e-283)
     (* x (/ 1.0 (* y a)))
     (if (<= b 4.8e-190)
       (/ (* b (- (/ x (* a b)) (/ x a))) y)
       (/ (/ x (+ a (* a b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+131) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= -9.5e-283) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 4.8e-190) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (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 (b <= (-5.8d+131)) then
        tmp = ((x * b) / a) / -y
    else if (b <= (-9.5d-283)) then
        tmp = x * (1.0d0 / (y * a))
    else if (b <= 4.8d-190) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (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 (b <= -5.8e+131) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= -9.5e-283) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 4.8e-190) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.8e+131:
		tmp = ((x * b) / a) / -y
	elif b <= -9.5e-283:
		tmp = x * (1.0 / (y * a))
	elif b <= 4.8e-190:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+131)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-y));
	elseif (b <= -9.5e-283)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 4.8e-190)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.8e+131)
		tmp = ((x * b) / a) / -y;
	elseif (b <= -9.5e-283)
		tmp = x * (1.0 / (y * a));
	elseif (b <= 4.8e-190)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+131], N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, -9.5e-283], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e-190], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.8000000000000002e131

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

   if -5.8000000000000002e131 < b < -9.49999999999999979e-283

   1. Initial program 96.2%

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

      1. associate-/l* 98.3%

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

      2. exp-diff 82.7%

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

      3. associate-/l/ 82.7%

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

      4. exp-sum 75.4%

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

      5. associate-/l* 74.2%

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

      6. *-commutative 74.2%

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

      7. exp-to-pow 74.2%

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

      8. *-commutative 74.2%

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

      9. exp-to-pow 74.6%

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

      10. sub-neg 74.6%

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

      11. metadata-eval 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around 0 72.4%

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

      1. exp-to-pow 72.8%

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

      2. sub-neg 72.8%

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

      3. metadata-eval 72.8%

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

      4. associate-/r* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in t around 0 48.7%

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

   9. Taylor expanded in b around 0 34.9%

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

       1. div-inv 37.3%

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

   11. Applied egg-rr 37.3%

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

   if -9.49999999999999979e-283 < b < 4.8000000000000001e-190

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. div-exp 74.3%

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

      2. exp-to-pow 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 40.7%

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

   7. Taylor expanded in b around 0 37.4%

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

      1. +-commutative 37.4%

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

      2. mul-1-neg 37.4%

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

      3. unsub-neg 37.4%

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

      4. associate-/l* 31.0%

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

   9. Simplified 31.0%

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

   10. Taylor expanded in b around inf 52.6%

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

   if 4.8000000000000001e-190 < b

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. div-exp 76.9%

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

      2. exp-to-pow 77.6%

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

      3. sub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around 0 69.3%

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

   7. Taylor expanded in b around 0 49.0%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.9% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+129)
   (/ (/ (* x b) a) (- y))
   (if (<= b 4.8e-251) (* x (/ 1.0 (* y a))) (/ (/ x (+ a (* a b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+129) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= 4.8e-251) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / (a + (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 (b <= (-2d+129)) then
        tmp = ((x * b) / a) / -y
    else if (b <= 4.8d-251) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / (a + (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 (b <= -2e+129) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= 4.8e-251) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+129:
		tmp = ((x * b) / a) / -y
	elif b <= 4.8e-251:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+129)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-y));
	elseif (b <= 4.8e-251)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+129)
		tmp = ((x * b) / a) / -y;
	elseif (b <= 4.8e-251)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+129], N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, 4.8e-251], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2e129

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

   if -2e129 < b < 4.79999999999999992e-251

   1. Initial program 96.7%

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

      1. associate-/l* 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. exp-diff 85.7%

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

      3. associate-/l/ 85.7%

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

      4. exp-sum 76.8%

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

      5. associate-/l* 75.9%

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

      6. *-commutative 75.9%

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

      7. exp-to-pow 75.9%

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

      8. *-commutative 75.9%

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

      9. exp-to-pow 76.4%

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

      10. sub-neg 76.4%

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

      11. metadata-eval 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in y around 0 72.5%

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

      1. exp-to-pow 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in t around 0 50.7%

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

   9. Taylor expanded in b around 0 39.4%

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

       1. div-inv 41.3%

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

   11. Applied egg-rr 41.3%

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

   if 4.79999999999999992e-251 < b

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. div-exp 76.8%

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

      2. exp-to-pow 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in t around 0 64.1%

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

   7. Taylor expanded in b around 0 45.9%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+138}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+138)
   (/ (* x b) (* y (- a)))
   (if (<= b 4.3e-249) (* x (/ 1.0 (* y a))) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+138) {
		tmp = (x * b) / (y * -a);
	} else if (b <= 4.3e-249) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.8d+138)) then
        tmp = (x * b) / (y * -a)
    else if (b <= 4.3d-249) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+138) {
		tmp = (x * b) / (y * -a);
	} else if (b <= 4.3e-249) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.8e+138:
		tmp = (x * b) / (y * -a)
	elif b <= 4.3e-249:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+138)
		tmp = Float64(Float64(x * b) / Float64(y * Float64(-a)));
	elseif (b <= 4.3e-249)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.8e+138)
		tmp = (x * b) / (y * -a);
	elseif (b <= 4.3e-249)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+138], N[(N[(x * b), $MachinePrecision] / N[(y * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e-249], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.80000000000000019e138

   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 97.2%

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

      1. div-exp 77.1%

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

      2. exp-to-pow 77.1%

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

      3. sub-neg 77.1%

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

      4. metadata-eval 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around 0 94.4%

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

   7. Taylor expanded in b around 0 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. associate-/l* 47.9%

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

   9. Simplified 47.9%

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

   10. Taylor expanded in b around inf 50.7%

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

   if -5.80000000000000019e138 < b < 4.3000000000000002e-249

   1. Initial program 96.7%

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

      1. associate-/l* 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. exp-diff 85.8%

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

      3. associate-/l/ 85.8%

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

      4. exp-sum 77.1%

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

      5. associate-/l* 76.1%

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

      6. *-commutative 76.1%

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

      7. exp-to-pow 76.1%

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

      8. *-commutative 76.1%

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

      9. exp-to-pow 76.6%

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

      10. sub-neg 76.6%

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

      11. metadata-eval 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in y around 0 72.8%

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

      1. exp-to-pow 73.3%

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

      2. sub-neg 73.3%

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

      3. metadata-eval 73.3%

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

      4. associate-/r* 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in t around 0 51.1%

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

   9. Taylor expanded in b around 0 39.1%

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

       1. div-inv 41.0%

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

   11. Applied egg-rr 41.0%

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

   if 4.3000000000000002e-249 < b

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. div-exp 76.8%

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

      2. exp-to-pow 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in t around 0 64.1%

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

   7. Taylor expanded in b around 0 39.5%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+138}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(-b\right)}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8e+136)
   (/ (* (/ x a) (- b)) y)
   (if (<= b 2.9e-244) (* x (/ 1.0 (* y a))) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+136) {
		tmp = ((x / a) * -b) / y;
	} else if (b <= 2.9e-244) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8d+136)) then
        tmp = ((x / a) * -b) / y
    else if (b <= 2.9d-244) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+136) {
		tmp = ((x / a) * -b) / y;
	} else if (b <= 2.9e-244) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8e+136:
		tmp = ((x / a) * -b) / y
	elif b <= 2.9e-244:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8e+136)
		tmp = Float64(Float64(Float64(x / a) * Float64(-b)) / y);
	elseif (b <= 2.9e-244)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8e+136)
		tmp = ((x / a) * -b) / y;
	elseif (b <= 2.9e-244)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8e+136], N[(N[(N[(x / a), $MachinePrecision] * (-b)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.9e-244], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.00000000000000047e136

   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 97.3%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

       1. neg-mul-1 57.4%

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

       2. associate-*r/ 46.7%

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

       3. *-commutative 46.7%

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

       4. distribute-rgt-neg-in 46.7%

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

   12. Simplified 46.7%

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

   if -8.00000000000000047e136 < b < 2.89999999999999996e-244

   1. Initial program 96.7%

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

      1. associate-/l* 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. exp-diff 85.7%

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

      3. associate-/l/ 85.7%

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

      4. exp-sum 76.8%

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

      5. associate-/l* 75.9%

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

      6. *-commutative 75.9%

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

      7. exp-to-pow 75.9%

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

      8. *-commutative 75.9%

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

      9. exp-to-pow 76.4%

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

      10. sub-neg 76.4%

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

      11. metadata-eval 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in y around 0 72.5%

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

      1. exp-to-pow 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in t around 0 50.7%

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

   9. Taylor expanded in b around 0 39.4%

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

       1. div-inv 41.3%

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

   11. Applied egg-rr 41.3%

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

   if 2.89999999999999996e-244 < b

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. div-exp 76.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 77.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 77.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 77.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 77.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 64.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 39.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(-b\right)}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e+106)
   (* (/ x (* y a)) (- b))
   (if (<= b 2.1e-245) (* x (/ 1.0 (* y a))) (/ (/ x a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+106) {
		tmp = (x / (y * a)) * -b;
	} else if (b <= 2.1e-245) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.4d+106)) then
        tmp = (x / (y * a)) * -b
    else if (b <= 2.1d-245) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+106) {
		tmp = (x / (y * a)) * -b;
	} else if (b <= 2.1e-245) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.4e+106:
		tmp = (x / (y * a)) * -b
	elif b <= 2.1e-245:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.4e+106)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(-b));
	elseif (b <= 2.1e-245)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.4e+106)
		tmp = (x / (y * a)) * -b;
	elseif (b <= 2.1e-245)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.4e+106], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, 2.1e-245], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.3999999999999996e106

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 91.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 70.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 70.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 70.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 70.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 70.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 84.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 49.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 49.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 49.6%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 49.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 40.9%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 40.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 43.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 43.0%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 38.9%

          \[\leadsto -\color{blue}{b \cdot \frac{x}{a \cdot y}} \]

       3. distribute-rgt-neg-in 38.9%

          \[\leadsto \color{blue}{b \cdot \left(-\frac{x}{a \cdot y}\right)} \]

       4. distribute-frac-neg2 38.9%

          \[\leadsto b \cdot \color{blue}{\frac{x}{-a \cdot y}} \]

       5. distribute-rgt-neg-in 38.9%

          \[\leadsto b \cdot \frac{x}{\color{blue}{a \cdot \left(-y\right)}} \]

   12. Simplified 38.9%

       \[\leadsto \color{blue}{b \cdot \frac{x}{a \cdot \left(-y\right)}} \]

   if -6.3999999999999996e106 < b < 2.1000000000000001e-245

   1. Initial program 96.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 90.8%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 90.8%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 81.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 80.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 80.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 80.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 80.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 80.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 80.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.5%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 76.1%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 76.1%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 76.1%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-/r* 75.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 75.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 51.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 41.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. div-inv 43.5%

          \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   11. Applied egg-rr 43.5%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   if 2.1000000000000001e-245 < b

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 76.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 77.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 77.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 77.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 77.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 64.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 39.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.3% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.9e-5) (/ (/ (* x b) a) (- 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 <= -3.9e-5) {
		tmp = ((x * b) / a) / -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 <= (-3.9d-5)) then
        tmp = ((x * b) / a) / -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 <= -3.9e-5) {
		tmp = ((x * b) / a) / -y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.9e-5:
		tmp = ((x * b) / a) / -y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.9e-5)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-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 <= -3.9e-5)
		tmp = ((x * b) / a) / -y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.9e-5], N[(N[(N[(x * b), $MachinePrecision] / a), $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 < -3.8999999999999999e-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. Add Preprocessing

   3. Taylor expanded in y around 0 86.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 67.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 67.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 67.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 67.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 78.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 40.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 40.9%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 40.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 35.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 35.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 40.9%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]

   if -3.8999999999999999e-5 < b

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 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. exp-diff 90.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 90.3%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 81.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 81.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 81.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 81.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 82.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 82.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 82.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 77.7%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 77.7%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-/r* 75.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 75.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 56.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 41.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 44.5%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 44.5%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 44.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.6% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.5e-5) (/ (* x b) (* 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 <= -5.5e-5) {
		tmp = (x * b) / (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 <= (-5.5d-5)) then
        tmp = (x * b) / (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 <= -5.5e-5) {
		tmp = (x * b) / (y * -a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.5e-5:
		tmp = (x * b) / (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 <= -5.5e-5)
		tmp = Float64(Float64(x * b) / Float64(y * Float64(-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 <= -5.5e-5)
		tmp = (x * b) / (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, -5.5e-5], N[(N[(x * b), $MachinePrecision] / N[(y * (-a)), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000002e-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. Add Preprocessing

   3. Taylor expanded in y around 0 86.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 67.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 67.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 67.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 67.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 78.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 40.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 40.9%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 40.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 35.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 35.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 36.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -5.5000000000000002e-5 < b

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 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. exp-diff 90.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 90.3%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 81.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 81.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 81.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 81.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 82.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 82.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 82.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 77.7%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 77.7%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-/r* 75.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 75.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 56.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 41.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 44.5%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 44.5%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 44.5%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.8% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.75e-245) (* x (/ 1.0 (* y a))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.75e-245) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.75d-245) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.75e-245) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.75e-245:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.75e-245)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.75e-245)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.75e-245], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.75000000000000008e-245

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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. exp-diff 82.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 82.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 72.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 71.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 71.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 71.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 71.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 71.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 71.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 71.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 74.3%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 74.3%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 74.3%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-/r* 72.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 62.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. div-inv 37.0%

          \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   11. Applied egg-rr 37.0%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

   if 1.75000000000000008e-245 < b

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 76.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 77.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 77.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 77.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 77.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 64.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 39.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.6% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.75e+49) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.75e+49) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.75d+49) then
        tmp = x / (y * a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.75e+49) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.75e+49:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.75e+49)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.75e+49)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.75e+49], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.7499999999999998e49

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 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. exp-diff 86.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 86.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 77.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. associate-/l* 75.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

      6. *-commutative 75.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      7. exp-to-pow 75.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

      8. *-commutative 75.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      9. exp-to-pow 76.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

      10. sub-neg 76.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

      11. metadata-eval 76.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 73.8%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 73.8%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 73.8%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-/r* 72.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 56.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 3.7499999999999998e49 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 80.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 80.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 80.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 80.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 80.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 86.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 37.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.75 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 31.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. exp-diff 83.9%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

   3. associate-/l/ 83.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

   4. exp-sum 75.7%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

   5. associate-/l* 74.5%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right)} \]

   6. *-commutative 74.5%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

   7. exp-to-pow 74.5%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}\right) \]

   8. *-commutative 74.5%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

   9. exp-to-pow 75.0%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right) \]

   10. sub-neg 75.0%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}}\right) \]

   11. metadata-eval 75.0%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}}\right) \]

3. Simplified 75.0%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 74.5%

   \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. exp-to-pow 75.0%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   2. sub-neg 75.0%

      \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   3. metadata-eval 75.0%

      \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   4. associate-/r* 72.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

7. Simplified 72.3%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

8. Taylor expanded in t around 0 62.3%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 34.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 34.8%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024096 
(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))