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

Percentage Accurate: 98.4% → 98.4%

Time: 35.5s

Alternatives: 31

Speedup: 1.0×

• 46.9% 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: 98.4% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

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

Alternative 2: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+20} \lor \neg \left(y \leq 6.8 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+20) (not (<= y 6.8e+79)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+20) || !(y <= 6.8e+79)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.1d+20)) .or. (.not. (y <= 6.8d+79))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+20) || !(y <= 6.8e+79)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.1e+20) or not (y <= 6.8e+79):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.1e+20) || !(y <= 6.8e+79))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.1e+20) || ~((y <= 6.8e+79)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.1e+20], N[Not[LessEqual[y, 6.8e+79]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e20 or 6.80000000000000063e79 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 95.7%

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

      1. +-commutative 95.7%

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

      2. mul-1-neg 95.7%

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

      3. unsub-neg 95.7%

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

   5. Simplified 95.7%

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

   if -4.1e20 < y < 6.80000000000000063e79

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 95.1%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+20} \lor \neg \left(y \leq 6.8 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+39} \lor \neg \left(y \leq 3 \cdot 10^{+205}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e+39) (not (<= y 3e+205)))
   (/ (/ (* 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 <= -2e+39) || !(y <= 3e+205)) {
		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 <= (-2d+39)) .or. (.not. (y <= 3d+205))) 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 <= -2e+39) || !(y <= 3e+205)) {
		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 <= -2e+39) or not (y <= 3e+205):
		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 <= -2e+39) || !(y <= 3e+205))
		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 <= -2e+39) || ~((y <= 3e+205)))
		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, -2e+39], N[Not[LessEqual[y, 3e+205]], $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 < -1.99999999999999988e39 or 2.9999999999999999e205 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 67.2%

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

      4. associate-/l* 61.2%

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

      5. *-commutative 61.2%

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

      6. exp-to-pow 61.2%

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

      7. exp-diff 49.3%

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

      8. *-commutative 49.3%

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

      9. exp-to-pow 49.3%

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

      10. sub-neg 49.3%

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

      11. metadata-eval 49.3%

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

   3. Simplified 49.3%

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

   5. Taylor expanded in b around 0 70.2%

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

      1. exp-to-pow 70.2%

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

      2. sub-neg 70.2%

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

      3. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in t around 0 94.1%

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

   if -1.99999999999999988e39 < y < 2.9999999999999999e205

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 91.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+39} \lor \neg \left(y \leq 3 \cdot 10^{+205}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+38} \lor \neg \left(y \leq 6.2 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.26e+38) (not (<= y 6.2e+49)))
   (/ (/ (* x (pow z y)) a) y)
   (* x (/ (/ (pow a (+ t -1.0)) (exp b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.26e+38) || !(y <= 6.2e+49)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = x * ((pow(a, (t + -1.0)) / 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 <= (-1.26d+38)) .or. (.not. (y <= 6.2d+49))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = x * (((a ** (t + (-1.0d0))) / 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 <= -1.26e+38) || !(y <= 6.2e+49)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = x * ((Math.pow(a, (t + -1.0)) / Math.exp(b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.26e+38) or not (y <= 6.2e+49):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = x * ((math.pow(a, (t + -1.0)) / math.exp(b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.26e+38) || !(y <= 6.2e+49))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.26e+38) || ~((y <= 6.2e+49)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = x * (((a ^ (t + -1.0)) / exp(b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.26e+38], N[Not[LessEqual[y, 6.2e+49]], $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] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25999999999999997e38 or 6.19999999999999985e49 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 64.2%

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

      4. associate-/l* 60.0%

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

      5. *-commutative 60.0%

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

      6. exp-to-pow 60.0%

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

      7. exp-diff 50.5%

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

      8. *-commutative 50.5%

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

      9. exp-to-pow 50.5%

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

      10. sub-neg 50.5%

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

      11. metadata-eval 50.5%

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

   3. Simplified 50.5%

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

   5. Taylor expanded in b around 0 65.4%

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

      1. exp-to-pow 65.4%

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

      2. sub-neg 65.4%

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

      3. metadata-eval 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in t around 0 85.5%

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

   if -1.25999999999999997e38 < y < 6.19999999999999985e49

   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. Add Preprocessing

   3. Taylor expanded in y around 0 94.4%

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

      1. associate-/l* 95.5%

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

      2. div-exp 84.4%

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

      3. exp-to-pow 85.8%

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

      4. sub-neg 85.8%

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

      5. metadata-eval 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+38} \lor \neg \left(y \leq 6.2 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+40} \lor \neg \left(t \leq 2.9 \cdot 10^{+62}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e+40) (not (<= t 2.9e+62)))
   (* x (/ (pow a (+ t -1.0)) y))
   (* x (/ (/ (pow z y) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+40) || !(t <= 2.9e+62)) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = x * ((pow(z, y) / 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 <= (-3d+40)) .or. (.not. (t <= 2.9d+62))) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = x * (((z ** y) / 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 <= -3e+40) || !(t <= 2.9e+62)) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = x * ((Math.pow(z, y) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e+40) or not (t <= 2.9e+62):
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = x * ((math.pow(z, y) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e+40) || !(t <= 2.9e+62))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / 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 <= -3e+40) || ~((t <= 2.9e+62)))
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = x * (((z ^ y) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e+40], N[Not[LessEqual[t, 2.9e+62]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0000000000000002e40 or 2.89999999999999984e62 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.9%

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

      1. associate-/l* 91.9%

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

      2. div-exp 68.9%

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

      3. exp-to-pow 68.9%

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

      4. sub-neg 68.9%

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

      5. metadata-eval 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in b around 0 84.6%

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

      1. exp-to-pow 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

   8. Simplified 84.6%

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

   if -3.0000000000000002e40 < t < 2.89999999999999984e62

   1. Initial program 95.9%

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

      1. associate-/l* 97.1%

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

      2. associate--l+ 97.1%

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

      3. exp-sum 81.4%

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

      4. associate-/l* 78.7%

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

      5. *-commutative 78.7%

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

      6. exp-to-pow 78.7%

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

      7. exp-diff 75.3%

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

      8. *-commutative 75.3%

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

      9. exp-to-pow 76.9%

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

      10. sub-neg 76.9%

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

      11. metadata-eval 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in t around 0 83.7%

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

      1. associate-/r* 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+40} \lor \neg \left(t \leq 2.9 \cdot 10^{+62}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -4e-6)
     t_1
     (if (<= y 2.3e-144)
       (/ x (* a (* y (exp b))))
       (if (<= y 1.6e+79) (* x (/ (pow a (+ t -1.0)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4e-6) {
		tmp = t_1;
	} else if (y <= 2.3e-144) {
		tmp = x / (a * (y * exp(b)));
	} else if (y <= 1.6e+79) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-4d-6)) then
        tmp = t_1
    else if (y <= 2.3d-144) then
        tmp = x / (a * (y * exp(b)))
    else if (y <= 1.6d+79) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4e-6) {
		tmp = t_1;
	} else if (y <= 2.3e-144) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (y <= 1.6e+79) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -4e-6:
		tmp = t_1
	elif y <= 2.3e-144:
		tmp = x / (a * (y * math.exp(b)))
	elif y <= 1.6e+79:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -4e-6)
		tmp = t_1;
	elseif (y <= 2.3e-144)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (y <= 1.6e+79)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -4e-6)
		tmp = t_1;
	elseif (y <= 2.3e-144)
		tmp = x / (a * (y * exp(b)));
	elseif (y <= 1.6e+79)
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4e-6], t$95$1, If[LessEqual[y, 2.3e-144], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+79], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999982e-6 or 1.60000000000000001e79 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 67.3%

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

      4. associate-/l* 63.4%

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

      5. *-commutative 63.4%

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

      6. exp-to-pow 63.4%

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

      7. exp-diff 54.5%

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

      8. *-commutative 54.5%

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

      9. exp-to-pow 54.5%

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

      10. sub-neg 54.5%

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

      11. metadata-eval 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in b around 0 69.4%

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

      1. exp-to-pow 69.4%

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

      2. sub-neg 69.4%

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

      3. metadata-eval 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in t around 0 85.4%

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

   if -3.99999999999999982e-6 < y < 2.3e-144

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 95.5%

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

      1. associate-/l* 96.4%

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

      2. div-exp 85.3%

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

      3. exp-to-pow 87.1%

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

      4. sub-neg 87.1%

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

      5. metadata-eval 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in t around 0 82.0%

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

   if 2.3e-144 < y < 1.60000000000000001e79

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. associate-/l* 97.0%

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

      2. div-exp 80.2%

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

      3. exp-to-pow 80.9%

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

      4. sub-neg 80.9%

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

      5. metadata-eval 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in b around 0 74.6%

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

      1. exp-to-pow 75.2%

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

      2. sub-neg 75.2%

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

      3. metadata-eval 75.2%

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

   8. Simplified 75.2%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{a}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -4e-6)
     t_1
     (if (<= y 3.15e-145)
       (/ (* x (/ (/ 1.0 a) (exp b))) y)
       (if (<= y 2.1e+79) (* x (/ (pow a (+ t -1.0)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4e-6) {
		tmp = t_1;
	} else if (y <= 3.15e-145) {
		tmp = (x * ((1.0 / a) / exp(b))) / y;
	} else if (y <= 2.1e+79) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-4d-6)) then
        tmp = t_1
    else if (y <= 3.15d-145) then
        tmp = (x * ((1.0d0 / a) / exp(b))) / y
    else if (y <= 2.1d+79) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4e-6) {
		tmp = t_1;
	} else if (y <= 3.15e-145) {
		tmp = (x * ((1.0 / a) / Math.exp(b))) / y;
	} else if (y <= 2.1e+79) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -4e-6:
		tmp = t_1
	elif y <= 3.15e-145:
		tmp = (x * ((1.0 / a) / math.exp(b))) / y
	elif y <= 2.1e+79:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -4e-6)
		tmp = t_1;
	elseif (y <= 3.15e-145)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) / exp(b))) / y);
	elseif (y <= 2.1e+79)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -4e-6)
		tmp = t_1;
	elseif (y <= 3.15e-145)
		tmp = (x * ((1.0 / a) / exp(b))) / y;
	elseif (y <= 2.1e+79)
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4e-6], t$95$1, If[LessEqual[y, 3.15e-145], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.1e+79], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999982e-6 or 2.10000000000000008e79 < 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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 67.3%

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

      4. associate-/l* 63.4%

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

      5. *-commutative 63.4%

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

      6. exp-to-pow 63.4%

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

      7. exp-diff 54.5%

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

      8. *-commutative 54.5%

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

      9. exp-to-pow 54.5%

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

      10. sub-neg 54.5%

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

      11. metadata-eval 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in b around 0 69.4%

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

      1. exp-to-pow 69.4%

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

      2. sub-neg 69.4%

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

      3. metadata-eval 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in t around 0 85.4%

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

   if -3.99999999999999982e-6 < y < 3.15e-145

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around 0 80.2%

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

      1. exp-neg 80.2%

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

      2. exp-sum 80.2%

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

      3. rem-exp-log 82.0%

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

      4. associate-/l/ 82.0%

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

   8. Simplified 82.0%

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

   if 3.15e-145 < y < 2.10000000000000008e79

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. associate-/l* 97.0%

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

      2. div-exp 80.2%

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

      3. exp-to-pow 80.9%

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

      4. sub-neg 80.9%

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

      5. metadata-eval 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in b around 0 74.6%

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

      1. exp-to-pow 75.2%

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

      2. sub-neg 75.2%

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

      3. metadata-eval 75.2%

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

   8. Simplified 75.2%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{a}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+56} \lor \neg \left(t \leq 2.3 \cdot 10^{+62}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4e+56) (not (<= t 2.3e+62)))
   (* 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 <= -4e+56) || !(t <= 2.3e+62)) {
		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 <= (-4d+56)) .or. (.not. (t <= 2.3d+62))) 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 <= -4e+56) || !(t <= 2.3e+62)) {
		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 <= -4e+56) or not (t <= 2.3e+62):
		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 ((t <= -4e+56) || !(t <= 2.3e+62))
		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 <= -4e+56) || ~((t <= 2.3e+62)))
		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[t, -4e+56], N[Not[LessEqual[t, 2.3e+62]], $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 t < -4.00000000000000037e56 or 2.29999999999999984e62 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.4%

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

      1. associate-/l* 91.4%

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

      2. div-exp 68.1%

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

      3. exp-to-pow 68.1%

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

      4. sub-neg 68.1%

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

      5. metadata-eval 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0 84.7%

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

      1. exp-to-pow 84.7%

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

      2. sub-neg 84.7%

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

      3. metadata-eval 84.7%

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

   8. Simplified 84.7%

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

   if -4.00000000000000037e56 < t < 2.29999999999999984e62

   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 71.3%

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

      1. associate-/l* 73.0%

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

      2. div-exp 68.5%

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

      3. exp-to-pow 70.0%

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

      4. sub-neg 70.0%

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

      5. metadata-eval 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in t around 0 74.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+56} \lor \neg \left(t \leq 2.3 \cdot 10^{+62}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+167}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e+167)
   (/ x (* b (* a (+ y (/ y b)))))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e+167) {
		tmp = x / (b * (a * (y + (y / b))));
	} 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 (y <= (-4.8d+167)) then
        tmp = x / (b * (a * (y + (y / b))))
    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 (y <= -4.8e+167) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.8e+167:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e+167)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	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 (y <= -4.8e+167)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e+167], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999998e167

   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 36.9%

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

      1. associate-/l* 36.7%

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

      2. div-exp 21.7%

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

      3. exp-to-pow 21.7%

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

      4. sub-neg 21.7%

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

      5. metadata-eval 21.7%

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

   5. Simplified 21.7%

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

   6. Taylor expanded in t around 0 17.1%

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

   7. Taylor expanded in b around 0 41.7%

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

   8. Taylor expanded in b around inf 46.7%

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

      1. associate-/l* 56.3%

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

      2. distribute-lft-out 61.3%

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

   10. Simplified 61.3%

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

   if -4.79999999999999998e167 < y

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 83.0%

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

      1. associate-/l* 84.1%

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

      2. div-exp 72.3%

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

      3. exp-to-pow 73.2%

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

      4. sub-neg 73.2%

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

      5. metadata-eval 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in t around 0 63.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+167}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ t_2 := \frac{x}{a \cdot \left(y \cdot b\right)}\\ t_3 := \frac{x}{y \cdot a}\\ t_4 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+126}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 + \frac{b}{a} \cdot -0.16666666666666666\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(t\_2 - t\_3\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-260}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{t\_3 - \frac{t\_3 - t\_2}{b}}{b}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          x
          (*
           a
           (+
            y
            (*
             b
             (+
              y
              (*
               b
               (+
                (* y 0.5)
                (*
                 b
                 (+
                  (* y 0.16666666666666666)
                  (*
                   b
                   (+
                    (* 0.008333333333333333 (* y b))
                    (* y 0.041666666666666664)))))))))))))
        (t_2 (/ x (* a (* y b))))
        (t_3 (/ x (* y a)))
        (t_4 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -1.65e+126)
     (/
      (*
       x
       (+
        (/ 1.0 a)
        (*
         b
         (+
          (* b (+ (* (/ 1.0 a) 0.5) (* (/ b a) -0.16666666666666666)))
          (/ -1.0 a)))))
      y)
     (if (<= b -4e-26)
       t_1
       (if (<= b -1.45e-157)
         (* b (- t_2 t_3))
         (if (<= b -6.4e-260)
           t_4
           (if (<= b 5.2e-224)
             (/ (/ x a) y)
             (if (<= b 4e-177)
               (/ (- t_3 (/ (- t_3 t_2) b)) b)
               (if (<= b 4.4e+18) t_4 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	double t_2 = x / (a * (y * b));
	double t_3 = x / (y * a);
	double t_4 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.65e+126) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y;
	} else if (b <= -4e-26) {
		tmp = t_1;
	} else if (b <= -1.45e-157) {
		tmp = b * (t_2 - t_3);
	} else if (b <= -6.4e-260) {
		tmp = t_4;
	} else if (b <= 5.2e-224) {
		tmp = (x / a) / y;
	} else if (b <= 4e-177) {
		tmp = (t_3 - ((t_3 - t_2) / b)) / b;
	} else if (b <= 4.4e+18) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (b * ((y * 0.16666666666666666d0) + (b * ((0.008333333333333333d0 * (y * b)) + (y * 0.041666666666666664d0)))))))))))
    t_2 = x / (a * (y * b))
    t_3 = x / (y * a)
    t_4 = x / (b * (a * (y + (y / b))))
    if (b <= (-1.65d+126)) then
        tmp = (x * ((1.0d0 / a) + (b * ((b * (((1.0d0 / a) * 0.5d0) + ((b / a) * (-0.16666666666666666d0)))) + ((-1.0d0) / a))))) / y
    else if (b <= (-4d-26)) then
        tmp = t_1
    else if (b <= (-1.45d-157)) then
        tmp = b * (t_2 - t_3)
    else if (b <= (-6.4d-260)) then
        tmp = t_4
    else if (b <= 5.2d-224) then
        tmp = (x / a) / y
    else if (b <= 4d-177) then
        tmp = (t_3 - ((t_3 - t_2) / b)) / b
    else if (b <= 4.4d+18) then
        tmp = t_4
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	double t_2 = x / (a * (y * b));
	double t_3 = x / (y * a);
	double t_4 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.65e+126) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y;
	} else if (b <= -4e-26) {
		tmp = t_1;
	} else if (b <= -1.45e-157) {
		tmp = b * (t_2 - t_3);
	} else if (b <= -6.4e-260) {
		tmp = t_4;
	} else if (b <= 5.2e-224) {
		tmp = (x / a) / y;
	} else if (b <= 4e-177) {
		tmp = (t_3 - ((t_3 - t_2) / b)) / b;
	} else if (b <= 4.4e+18) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))))
	t_2 = x / (a * (y * b))
	t_3 = x / (y * a)
	t_4 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -1.65e+126:
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y
	elif b <= -4e-26:
		tmp = t_1
	elif b <= -1.45e-157:
		tmp = b * (t_2 - t_3)
	elif b <= -6.4e-260:
		tmp = t_4
	elif b <= 5.2e-224:
		tmp = (x / a) / y
	elif b <= 4e-177:
		tmp = (t_3 - ((t_3 - t_2) / b)) / b
	elif b <= 4.4e+18:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(b * Float64(Float64(y * 0.16666666666666666) + Float64(b * Float64(Float64(0.008333333333333333 * Float64(y * b)) + Float64(y * 0.041666666666666664))))))))))))
	t_2 = Float64(x / Float64(a * Float64(y * b)))
	t_3 = Float64(x / Float64(y * a))
	t_4 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -1.65e+126)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(1.0 / a) * 0.5) + Float64(Float64(b / a) * -0.16666666666666666))) + Float64(-1.0 / a))))) / y);
	elseif (b <= -4e-26)
		tmp = t_1;
	elseif (b <= -1.45e-157)
		tmp = Float64(b * Float64(t_2 - t_3));
	elseif (b <= -6.4e-260)
		tmp = t_4;
	elseif (b <= 5.2e-224)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4e-177)
		tmp = Float64(Float64(t_3 - Float64(Float64(t_3 - t_2) / b)) / b);
	elseif (b <= 4.4e+18)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	t_2 = x / (a * (y * b));
	t_3 = x / (y * a);
	t_4 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -1.65e+126)
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y;
	elseif (b <= -4e-26)
		tmp = t_1;
	elseif (b <= -1.45e-157)
		tmp = b * (t_2 - t_3);
	elseif (b <= -6.4e-260)
		tmp = t_4;
	elseif (b <= 5.2e-224)
		tmp = (x / a) / y;
	elseif (b <= 4e-177)
		tmp = (t_3 - ((t_3 - t_2) / b)) / b;
	elseif (b <= 4.4e+18)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(b * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(b * N[(N[(0.008333333333333333 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+126], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(N[(b / a), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -4e-26], t$95$1, If[LessEqual[b, -1.45e-157], N[(b * N[(t$95$2 - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.4e-260], t$95$4, If[LessEqual[b, 5.2e-224], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4e-177], N[(N[(t$95$3 - N[(N[(t$95$3 - t$95$2), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, 4.4e+18], t$95$4, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.65000000000000006e126

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.0%

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

      1. +-commutative 93.0%

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

      2. mul-1-neg 93.0%

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

      3. unsub-neg 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in y around 0 85.9%

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

      1. exp-neg 85.9%

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

      2. exp-sum 85.9%

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

      3. rem-exp-log 85.9%

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

      4. associate-/l/ 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in b around 0 85.9%

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

   if -1.65000000000000006e126 < b < -4.0000000000000002e-26 or 4.4e18 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.9%

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

      1. associate-/l* 88.9%

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

      2. div-exp 66.6%

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

      3. exp-to-pow 66.8%

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

      4. sub-neg 66.8%

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

      5. metadata-eval 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in t around 0 76.2%

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

   7. Taylor expanded in b around 0 65.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.5 \cdot y + b \cdot \left(0.16666666666666666 \cdot y + b \cdot \left(0.008333333333333333 \cdot \left(b \cdot y\right) + 0.041666666666666664 \cdot y\right)\right)\right)\right)\right)}} \]

   if -4.0000000000000002e-26 < b < -1.44999999999999994e-157

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. exp-neg 45.2%

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

      2. exp-sum 45.2%

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

      3. rem-exp-log 46.8%

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

      4. associate-/l/ 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in b around 0 46.8%

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

   10. Taylor expanded in b around inf 50.0%

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

       1. mul-1-neg 50.0%

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

       2. +-commutative 50.0%

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

       3. sub-neg 50.0%

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

       4. *-commutative 50.0%

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

   12. Simplified 50.0%

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

   if -1.44999999999999994e-157 < b < -6.3999999999999999e-260 or 3.99999999999999981e-177 < b < 4.4e18

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 63.0%

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

      1. associate-/l* 67.5%

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

      2. div-exp 64.1%

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

      3. exp-to-pow 65.2%

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

      4. sub-neg 65.2%

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

      5. metadata-eval 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 40.0%

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

   8. Taylor expanded in b around inf 46.5%

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

      1. associate-/l* 49.9%

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

      2. distribute-lft-out 51.8%

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

   10. Simplified 51.8%

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

   if -6.3999999999999999e-260 < b < 5.2000000000000004e-224

   1. Initial program 94.0%

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

      1. associate-/l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. exp-sum 86.3%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 86.3%

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

      10. sub-neg 86.3%

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

      11. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 83.6%

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

   9. Taylor expanded in y around 0 56.9%

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

   if 5.2000000000000004e-224 < b < 3.99999999999999981e-177

   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 14.8%

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

      1. associate-/l* 14.8%

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

      2. div-exp 14.8%

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

      3. exp-to-pow 14.8%

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

      4. sub-neg 14.8%

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

      5. metadata-eval 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in t around 0 3.4%

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

   7. Taylor expanded in b around 0 3.4%

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

   8. Taylor expanded in b around -inf 39.9%

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

      1. mul-1-neg 39.9%

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

   10. Simplified 39.9%

       \[\leadsto \color{blue}{-\frac{\left(-\frac{\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{a \cdot y}}{b}\right) - \frac{x}{a \cdot y}}{b}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+126}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 + \frac{b}{a} \cdot -0.16666666666666666\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a} - \frac{\frac{x}{y \cdot a} - \frac{x}{a \cdot \left(y \cdot b\right)}}{b}}{b}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.9% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 - b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 - \frac{b}{a} \cdot 0.041666666666666664\right)\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{t\_1 + \frac{\frac{t\_1 + \frac{\frac{x}{b \cdot \left(y \cdot a\right)} - t\_1}{b}}{b} - t\_1}{b}}{b}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -1.75e-157)
     (/
      (*
       x
       (+
        (/ 1.0 a)
        (*
         b
         (+
          (*
           b
           (-
            (* (/ 1.0 a) 0.5)
            (*
             b
             (-
              (* (/ 1.0 a) 0.16666666666666666)
              (* (/ b a) 0.041666666666666664)))))
          (/ -1.0 a)))))
      y)
     (if (<= b -5e-263)
       t_2
       (if (<= b 2.9e-223)
         (/ (/ x a) y)
         (if (<= b 9.2e-176)
           (/
            (+
             t_1
             (/ (- (/ (+ t_1 (/ (- (/ x (* b (* y a))) t_1) b)) b) t_1) b))
            b)
           (if (<= b 6.6e+18)
             t_2
             (/
              x
              (*
               a
               (+
                y
                (*
                 b
                 (+
                  y
                  (*
                   b
                   (+
                    (* y 0.5)
                    (*
                     b
                     (+
                      (* y 0.16666666666666666)
                      (*
                       b
                       (+
                        (* 0.008333333333333333 (* y b))
                        (* y 0.041666666666666664)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.75e-157) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	} else if (b <= -5e-263) {
		tmp = t_2;
	} else if (b <= 2.9e-223) {
		tmp = (x / a) / y;
	} else if (b <= 9.2e-176) {
		tmp = (t_1 + ((((t_1 + (((x / (b * (y * a))) - t_1) / b)) / b) - t_1) / b)) / b;
	} else if (b <= 6.6e+18) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = x / (b * (a * (y + (y / b))))
    if (b <= (-1.75d-157)) then
        tmp = (x * ((1.0d0 / a) + (b * ((b * (((1.0d0 / a) * 0.5d0) - (b * (((1.0d0 / a) * 0.16666666666666666d0) - ((b / a) * 0.041666666666666664d0))))) + ((-1.0d0) / a))))) / y
    else if (b <= (-5d-263)) then
        tmp = t_2
    else if (b <= 2.9d-223) then
        tmp = (x / a) / y
    else if (b <= 9.2d-176) then
        tmp = (t_1 + ((((t_1 + (((x / (b * (y * a))) - t_1) / b)) / b) - t_1) / b)) / b
    else if (b <= 6.6d+18) then
        tmp = t_2
    else
        tmp = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (b * ((y * 0.16666666666666666d0) + (b * ((0.008333333333333333d0 * (y * b)) + (y * 0.041666666666666664d0)))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.75e-157) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	} else if (b <= -5e-263) {
		tmp = t_2;
	} else if (b <= 2.9e-223) {
		tmp = (x / a) / y;
	} else if (b <= 9.2e-176) {
		tmp = (t_1 + ((((t_1 + (((x / (b * (y * a))) - t_1) / b)) / b) - t_1) / b)) / b;
	} else if (b <= 6.6e+18) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -1.75e-157:
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y
	elif b <= -5e-263:
		tmp = t_2
	elif b <= 2.9e-223:
		tmp = (x / a) / y
	elif b <= 9.2e-176:
		tmp = (t_1 + ((((t_1 + (((x / (b * (y * a))) - t_1) / b)) / b) - t_1) / b)) / b
	elif b <= 6.6e+18:
		tmp = t_2
	else:
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -1.75e-157)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(1.0 / a) * 0.5) - Float64(b * Float64(Float64(Float64(1.0 / a) * 0.16666666666666666) - Float64(Float64(b / a) * 0.041666666666666664))))) + Float64(-1.0 / a))))) / y);
	elseif (b <= -5e-263)
		tmp = t_2;
	elseif (b <= 2.9e-223)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 9.2e-176)
		tmp = Float64(Float64(t_1 + Float64(Float64(Float64(Float64(t_1 + Float64(Float64(Float64(x / Float64(b * Float64(y * a))) - t_1) / b)) / b) - t_1) / b)) / b);
	elseif (b <= 6.6e+18)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(b * Float64(Float64(y * 0.16666666666666666) + Float64(b * Float64(Float64(0.008333333333333333 * Float64(y * b)) + Float64(y * 0.041666666666666664))))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -1.75e-157)
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	elseif (b <= -5e-263)
		tmp = t_2;
	elseif (b <= 2.9e-223)
		tmp = (x / a) / y;
	elseif (b <= 9.2e-176)
		tmp = (t_1 + ((((t_1 + (((x / (b * (y * a))) - t_1) / b)) / b) - t_1) / b)) / b;
	elseif (b <= 6.6e+18)
		tmp = t_2;
	else
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e-157], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.5), $MachinePrecision] - N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -5e-263], t$95$2, If[LessEqual[b, 2.9e-223], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 9.2e-176], N[(N[(t$95$1 + N[(N[(N[(N[(t$95$1 + N[(N[(N[(x / N[(b * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$1), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, 6.6e+18], t$95$2, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(b * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(b * N[(N[(0.008333333333333333 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.7500000000000001e-157

   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 t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. exp-neg 61.0%

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

      2. exp-sum 60.9%

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

      3. rem-exp-log 61.7%

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

      4. associate-/l/ 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in b around 0 56.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(b \cdot \left(0.041666666666666664 \cdot \frac{b}{a} - 0.16666666666666666 \cdot \frac{1}{a}\right) + 0.5 \cdot \frac{1}{a}\right) - \frac{1}{a}\right) + \frac{1}{a}\right)}}{y} \]

   if -1.7500000000000001e-157 < b < -5.00000000000000006e-263 or 9.2000000000000005e-176 < b < 6.6e18

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 63.0%

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

      1. associate-/l* 67.5%

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

      2. div-exp 64.1%

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

      3. exp-to-pow 65.2%

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

      4. sub-neg 65.2%

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

      5. metadata-eval 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 40.0%

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

   8. Taylor expanded in b around inf 46.5%

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

      1. associate-/l* 49.9%

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

      2. distribute-lft-out 51.8%

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

   10. Simplified 51.8%

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

   if -5.00000000000000006e-263 < b < 2.9e-223

   1. Initial program 94.0%

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

      1. associate-/l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. exp-sum 86.3%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 86.3%

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

      10. sub-neg 86.3%

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

      11. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 83.6%

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

   9. Taylor expanded in y around 0 56.9%

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

   if 2.9e-223 < b < 9.2000000000000005e-176

   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 14.8%

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

      1. associate-/l* 14.8%

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

      2. div-exp 14.8%

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

      3. exp-to-pow 14.8%

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

      4. sub-neg 14.8%

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

      5. metadata-eval 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in t around 0 3.4%

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

   7. Taylor expanded in b around 0 3.4%

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

   8. Taylor expanded in b around -inf 63.1%

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

   10. Simplified 50.8%

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

   if 6.6e18 < 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 92.2%

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

      1. associate-/l* 92.2%

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

      2. div-exp 69.9%

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

      3. exp-to-pow 69.9%

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

      4. sub-neg 69.9%

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

      5. metadata-eval 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around 0 87.5%

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

   7. Taylor expanded in b around 0 75.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.5 \cdot y + b \cdot \left(0.16666666666666666 \cdot y + b \cdot \left(0.008333333333333333 \cdot \left(b \cdot y\right) + 0.041666666666666664 \cdot y\right)\right)\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 - b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 - \frac{b}{a} \cdot 0.041666666666666664\right)\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a} + \frac{\frac{\frac{x}{y \cdot a} + \frac{\frac{x}{b \cdot \left(y \cdot a\right)} - \frac{x}{y \cdot a}}{b}}{b} - \frac{x}{y \cdot a}}{b}}{b}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.9% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{-162}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 - b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 - \frac{b}{a} \cdot 0.041666666666666664\right)\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-177}:\\ \;\;\;\;\frac{t\_1 - \frac{t\_1 + \frac{\frac{t\_1 - \frac{x}{a \cdot \left(y \cdot b\right)}}{b} - t\_1}{b}}{b}}{b}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -1.35e-162)
     (/
      (*
       x
       (+
        (/ 1.0 a)
        (*
         b
         (+
          (*
           b
           (-
            (* (/ 1.0 a) 0.5)
            (*
             b
             (-
              (* (/ 1.0 a) 0.16666666666666666)
              (* (/ b a) 0.041666666666666664)))))
          (/ -1.0 a)))))
      y)
     (if (<= b -1.75e-261)
       t_2
       (if (<= b 3.2e-223)
         (/ (/ x a) y)
         (if (<= b 4.2e-177)
           (/
            (-
             t_1
             (/ (+ t_1 (/ (- (/ (- t_1 (/ x (* a (* y b)))) b) t_1) b)) b))
            b)
           (if (<= b 4.3e+18)
             t_2
             (/
              x
              (*
               a
               (+
                y
                (*
                 b
                 (+
                  y
                  (*
                   b
                   (+
                    (* y 0.5)
                    (*
                     b
                     (+
                      (* y 0.16666666666666666)
                      (*
                       b
                       (+
                        (* 0.008333333333333333 (* y b))
                        (* y 0.041666666666666664)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.35e-162) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	} else if (b <= -1.75e-261) {
		tmp = t_2;
	} else if (b <= 3.2e-223) {
		tmp = (x / a) / y;
	} else if (b <= 4.2e-177) {
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b;
	} else if (b <= 4.3e+18) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = x / (b * (a * (y + (y / b))))
    if (b <= (-1.35d-162)) then
        tmp = (x * ((1.0d0 / a) + (b * ((b * (((1.0d0 / a) * 0.5d0) - (b * (((1.0d0 / a) * 0.16666666666666666d0) - ((b / a) * 0.041666666666666664d0))))) + ((-1.0d0) / a))))) / y
    else if (b <= (-1.75d-261)) then
        tmp = t_2
    else if (b <= 3.2d-223) then
        tmp = (x / a) / y
    else if (b <= 4.2d-177) then
        tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b
    else if (b <= 4.3d+18) then
        tmp = t_2
    else
        tmp = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (b * ((y * 0.16666666666666666d0) + (b * ((0.008333333333333333d0 * (y * b)) + (y * 0.041666666666666664d0)))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.35e-162) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	} else if (b <= -1.75e-261) {
		tmp = t_2;
	} else if (b <= 3.2e-223) {
		tmp = (x / a) / y;
	} else if (b <= 4.2e-177) {
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b;
	} else if (b <= 4.3e+18) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -1.35e-162:
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y
	elif b <= -1.75e-261:
		tmp = t_2
	elif b <= 3.2e-223:
		tmp = (x / a) / y
	elif b <= 4.2e-177:
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b
	elif b <= 4.3e+18:
		tmp = t_2
	else:
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -1.35e-162)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(1.0 / a) * 0.5) - Float64(b * Float64(Float64(Float64(1.0 / a) * 0.16666666666666666) - Float64(Float64(b / a) * 0.041666666666666664))))) + Float64(-1.0 / a))))) / y);
	elseif (b <= -1.75e-261)
		tmp = t_2;
	elseif (b <= 3.2e-223)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4.2e-177)
		tmp = Float64(Float64(t_1 - Float64(Float64(t_1 + Float64(Float64(Float64(Float64(t_1 - Float64(x / Float64(a * Float64(y * b)))) / b) - t_1) / b)) / b)) / b);
	elseif (b <= 4.3e+18)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(b * Float64(Float64(y * 0.16666666666666666) + Float64(b * Float64(Float64(0.008333333333333333 * Float64(y * b)) + Float64(y * 0.041666666666666664))))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -1.35e-162)
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	elseif (b <= -1.75e-261)
		tmp = t_2;
	elseif (b <= 3.2e-223)
		tmp = (x / a) / y;
	elseif (b <= 4.2e-177)
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b;
	elseif (b <= 4.3e+18)
		tmp = t_2;
	else
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e-162], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.5), $MachinePrecision] - N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.75e-261], t$95$2, If[LessEqual[b, 3.2e-223], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.2e-177], N[(N[(t$95$1 - N[(N[(t$95$1 + N[(N[(N[(N[(t$95$1 - N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$1), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, 4.3e+18], t$95$2, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(b * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(b * N[(N[(0.008333333333333333 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.34999999999999992e-162

   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 t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. exp-neg 61.0%

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

      2. exp-sum 60.9%

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

      3. rem-exp-log 61.7%

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

      4. associate-/l/ 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in b around 0 56.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(b \cdot \left(0.041666666666666664 \cdot \frac{b}{a} - 0.16666666666666666 \cdot \frac{1}{a}\right) + 0.5 \cdot \frac{1}{a}\right) - \frac{1}{a}\right) + \frac{1}{a}\right)}}{y} \]

   if -1.34999999999999992e-162 < b < -1.7499999999999999e-261 or 4.20000000000000002e-177 < b < 4.3e18

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 63.0%

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

      1. associate-/l* 67.5%

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

      2. div-exp 64.1%

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

      3. exp-to-pow 65.2%

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

      4. sub-neg 65.2%

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

      5. metadata-eval 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 40.0%

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

   8. Taylor expanded in b around inf 46.5%

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

      1. associate-/l* 49.9%

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

      2. distribute-lft-out 51.8%

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

   10. Simplified 51.8%

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

   if -1.7499999999999999e-261 < b < 3.2000000000000001e-223

   1. Initial program 94.0%

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

      1. associate-/l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. exp-sum 86.3%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 86.3%

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

      10. sub-neg 86.3%

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

      11. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 83.6%

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

   9. Taylor expanded in y around 0 56.9%

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

   if 3.2000000000000001e-223 < b < 4.20000000000000002e-177

   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 14.8%

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

      1. associate-/l* 14.8%

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

      2. div-exp 14.8%

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

      3. exp-to-pow 14.8%

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

      4. sub-neg 14.8%

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

      5. metadata-eval 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in t around 0 3.4%

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

   7. Taylor expanded in b around 0 3.4%

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

   8. Taylor expanded in b around -inf 63.1%

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

   10. Simplified 63.1%

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

   if 4.3e18 < 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 92.2%

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

      1. associate-/l* 92.2%

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

      2. div-exp 69.9%

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

      3. exp-to-pow 69.9%

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

      4. sub-neg 69.9%

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

      5. metadata-eval 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around 0 87.5%

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

   7. Taylor expanded in b around 0 75.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.5 \cdot y + b \cdot \left(0.16666666666666666 \cdot y + b \cdot \left(0.008333333333333333 \cdot \left(b \cdot y\right) + 0.041666666666666664 \cdot y\right)\right)\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-162}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 - b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 - \frac{b}{a} \cdot 0.041666666666666664\right)\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a} - \frac{\frac{x}{y \cdot a} + \frac{\frac{\frac{x}{y \cdot a} - \frac{x}{a \cdot \left(y \cdot b\right)}}{b} - \frac{x}{y \cdot a}}{b}}{b}}{b}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.4% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - b \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 + b \cdot \left(0.041666666666666664 \cdot \frac{-1}{a} - -0.008333333333333333 \cdot \frac{b}{a}\right)\right) + 0.5 \cdot \frac{-1}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-264}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{t\_1 - \frac{t\_1 + \frac{\frac{t\_1 - \frac{x}{a \cdot \left(y \cdot b\right)}}{b} - t\_1}{b}}{b}}{b}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -2e-161)
     (/
      (*
       x
       (-
        (/ 1.0 a)
        (*
         b
         (+
          (/ 1.0 a)
          (*
           b
           (+
            (*
             b
             (+
              (* (/ 1.0 a) 0.16666666666666666)
              (*
               b
               (-
                (* 0.041666666666666664 (/ -1.0 a))
                (* -0.008333333333333333 (/ b a))))))
            (* 0.5 (/ -1.0 a))))))))
      y)
     (if (<= b -1e-264)
       t_2
       (if (<= b 2.1e-223)
         (/ (/ x a) y)
         (if (<= b 4e-177)
           (/
            (-
             t_1
             (/ (+ t_1 (/ (- (/ (- t_1 (/ x (* a (* y b)))) b) t_1) b)) b))
            b)
           (if (<= b 1.5e+19)
             t_2
             (/
              x
              (*
               a
               (+
                y
                (*
                 b
                 (+
                  y
                  (*
                   b
                   (+
                    (* y 0.5)
                    (*
                     b
                     (+
                      (* y 0.16666666666666666)
                      (*
                       b
                       (+
                        (* 0.008333333333333333 (* y b))
                        (* y 0.041666666666666664)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -2e-161) {
		tmp = (x * ((1.0 / a) - (b * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.16666666666666666) + (b * ((0.041666666666666664 * (-1.0 / a)) - (-0.008333333333333333 * (b / a)))))) + (0.5 * (-1.0 / a)))))))) / y;
	} else if (b <= -1e-264) {
		tmp = t_2;
	} else if (b <= 2.1e-223) {
		tmp = (x / a) / y;
	} else if (b <= 4e-177) {
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b;
	} else if (b <= 1.5e+19) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = x / (b * (a * (y + (y / b))))
    if (b <= (-2d-161)) then
        tmp = (x * ((1.0d0 / a) - (b * ((1.0d0 / a) + (b * ((b * (((1.0d0 / a) * 0.16666666666666666d0) + (b * ((0.041666666666666664d0 * ((-1.0d0) / a)) - ((-0.008333333333333333d0) * (b / a)))))) + (0.5d0 * ((-1.0d0) / a)))))))) / y
    else if (b <= (-1d-264)) then
        tmp = t_2
    else if (b <= 2.1d-223) then
        tmp = (x / a) / y
    else if (b <= 4d-177) then
        tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b
    else if (b <= 1.5d+19) then
        tmp = t_2
    else
        tmp = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (b * ((y * 0.16666666666666666d0) + (b * ((0.008333333333333333d0 * (y * b)) + (y * 0.041666666666666664d0)))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -2e-161) {
		tmp = (x * ((1.0 / a) - (b * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.16666666666666666) + (b * ((0.041666666666666664 * (-1.0 / a)) - (-0.008333333333333333 * (b / a)))))) + (0.5 * (-1.0 / a)))))))) / y;
	} else if (b <= -1e-264) {
		tmp = t_2;
	} else if (b <= 2.1e-223) {
		tmp = (x / a) / y;
	} else if (b <= 4e-177) {
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b;
	} else if (b <= 1.5e+19) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -2e-161:
		tmp = (x * ((1.0 / a) - (b * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.16666666666666666) + (b * ((0.041666666666666664 * (-1.0 / a)) - (-0.008333333333333333 * (b / a)))))) + (0.5 * (-1.0 / a)))))))) / y
	elif b <= -1e-264:
		tmp = t_2
	elif b <= 2.1e-223:
		tmp = (x / a) / y
	elif b <= 4e-177:
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b
	elif b <= 1.5e+19:
		tmp = t_2
	else:
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -2e-161)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(1.0 / a) * 0.16666666666666666) + Float64(b * Float64(Float64(0.041666666666666664 * Float64(-1.0 / a)) - Float64(-0.008333333333333333 * Float64(b / a)))))) + Float64(0.5 * Float64(-1.0 / a)))))))) / y);
	elseif (b <= -1e-264)
		tmp = t_2;
	elseif (b <= 2.1e-223)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4e-177)
		tmp = Float64(Float64(t_1 - Float64(Float64(t_1 + Float64(Float64(Float64(Float64(t_1 - Float64(x / Float64(a * Float64(y * b)))) / b) - t_1) / b)) / b)) / b);
	elseif (b <= 1.5e+19)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(b * Float64(Float64(y * 0.16666666666666666) + Float64(b * Float64(Float64(0.008333333333333333 * Float64(y * b)) + Float64(y * 0.041666666666666664))))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -2e-161)
		tmp = (x * ((1.0 / a) - (b * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.16666666666666666) + (b * ((0.041666666666666664 * (-1.0 / a)) - (-0.008333333333333333 * (b / a)))))) + (0.5 * (-1.0 / a)))))))) / y;
	elseif (b <= -1e-264)
		tmp = t_2;
	elseif (b <= 2.1e-223)
		tmp = (x / a) / y;
	elseif (b <= 4e-177)
		tmp = (t_1 - ((t_1 + ((((t_1 - (x / (a * (y * b)))) / b) - t_1) / b)) / b)) / b;
	elseif (b <= 1.5e+19)
		tmp = t_2;
	else
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e-161], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(b * N[(N[(0.041666666666666664 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] - N[(-0.008333333333333333 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1e-264], t$95$2, If[LessEqual[b, 2.1e-223], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4e-177], N[(N[(t$95$1 - N[(N[(t$95$1 + N[(N[(N[(N[(t$95$1 - N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$1), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, 1.5e+19], t$95$2, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(b * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(b * N[(N[(0.008333333333333333 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.00000000000000006e-161

   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 t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. exp-neg 61.0%

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

      2. exp-sum 60.9%

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

      3. rem-exp-log 61.7%

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

      4. associate-/l/ 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in b around 0 58.6%

      \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(b \cdot \left(b \cdot \left(-0.008333333333333333 \cdot \frac{b}{a} + 0.041666666666666664 \cdot \frac{1}{a}\right) - 0.16666666666666666 \cdot \frac{1}{a}\right) + 0.5 \cdot \frac{1}{a}\right) - \frac{1}{a}\right) + \frac{1}{a}\right)}}{y} \]

   if -2.00000000000000006e-161 < b < -1e-264 or 3.99999999999999981e-177 < b < 1.5e19

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 63.0%

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

      1. associate-/l* 67.5%

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

      2. div-exp 64.1%

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

      3. exp-to-pow 65.2%

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

      4. sub-neg 65.2%

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

      5. metadata-eval 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 40.0%

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

   8. Taylor expanded in b around inf 46.5%

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

      1. associate-/l* 49.9%

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

      2. distribute-lft-out 51.8%

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

   10. Simplified 51.8%

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

   if -1e-264 < b < 2.09999999999999982e-223

   1. Initial program 94.0%

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

      1. associate-/l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. exp-sum 86.3%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 86.3%

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

      10. sub-neg 86.3%

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

      11. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 83.6%

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

   9. Taylor expanded in y around 0 56.9%

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

   if 2.09999999999999982e-223 < b < 3.99999999999999981e-177

   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 14.8%

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

      1. associate-/l* 14.8%

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

      2. div-exp 14.8%

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

      3. exp-to-pow 14.8%

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

      4. sub-neg 14.8%

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

      5. metadata-eval 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in t around 0 3.4%

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

   7. Taylor expanded in b around 0 3.4%

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

   8. Taylor expanded in b around -inf 63.1%

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

   10. Simplified 63.1%

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

   if 1.5e19 < 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 92.2%

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

      1. associate-/l* 92.2%

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

      2. div-exp 69.9%

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

      3. exp-to-pow 69.9%

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

      4. sub-neg 69.9%

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

      5. metadata-eval 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around 0 87.5%

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

   7. Taylor expanded in b around 0 75.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.5 \cdot y + b \cdot \left(0.16666666666666666 \cdot y + b \cdot \left(0.008333333333333333 \cdot \left(b \cdot y\right) + 0.041666666666666664 \cdot y\right)\right)\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - b \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 + b \cdot \left(0.041666666666666664 \cdot \frac{-1}{a} - -0.008333333333333333 \cdot \frac{b}{a}\right)\right) + 0.5 \cdot \frac{-1}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a} - \frac{\frac{x}{y \cdot a} + \frac{\frac{\frac{x}{y \cdot a} - \frac{x}{a \cdot \left(y \cdot b\right)}}{b} - \frac{x}{y \cdot a}}{b}}{b}}{b}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.8% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{-155}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 - b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 - \frac{b}{a} \cdot 0.041666666666666664\right)\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-262}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-177}:\\ \;\;\;\;\frac{t\_1 - \frac{t\_1 - \frac{x}{a \cdot \left(y \cdot b\right)}}{b}}{b}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= b -1.4e-155)
     (/
      (*
       x
       (+
        (/ 1.0 a)
        (*
         b
         (+
          (*
           b
           (-
            (* (/ 1.0 a) 0.5)
            (*
             b
             (-
              (* (/ 1.0 a) 0.16666666666666666)
              (* (/ b a) 0.041666666666666664)))))
          (/ -1.0 a)))))
      y)
     (if (<= b -1.35e-262)
       t_2
       (if (<= b 8.2e-224)
         (/ (/ x a) y)
         (if (<= b 4.8e-177)
           (/ (- t_1 (/ (- t_1 (/ x (* a (* y b)))) b)) b)
           (if (<= b 6.8e+18)
             t_2
             (/
              x
              (*
               a
               (+
                y
                (*
                 b
                 (+
                  y
                  (*
                   b
                   (+
                    (* y 0.5)
                    (*
                     b
                     (+
                      (* y 0.16666666666666666)
                      (*
                       b
                       (+
                        (* 0.008333333333333333 (* y b))
                        (* y 0.041666666666666664)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.4e-155) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	} else if (b <= -1.35e-262) {
		tmp = t_2;
	} else if (b <= 8.2e-224) {
		tmp = (x / a) / y;
	} else if (b <= 4.8e-177) {
		tmp = (t_1 - ((t_1 - (x / (a * (y * b)))) / b)) / b;
	} else if (b <= 6.8e+18) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = x / (b * (a * (y + (y / b))))
    if (b <= (-1.4d-155)) then
        tmp = (x * ((1.0d0 / a) + (b * ((b * (((1.0d0 / a) * 0.5d0) - (b * (((1.0d0 / a) * 0.16666666666666666d0) - ((b / a) * 0.041666666666666664d0))))) + ((-1.0d0) / a))))) / y
    else if (b <= (-1.35d-262)) then
        tmp = t_2
    else if (b <= 8.2d-224) then
        tmp = (x / a) / y
    else if (b <= 4.8d-177) then
        tmp = (t_1 - ((t_1 - (x / (a * (y * b)))) / b)) / b
    else if (b <= 6.8d+18) then
        tmp = t_2
    else
        tmp = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (b * ((y * 0.16666666666666666d0) + (b * ((0.008333333333333333d0 * (y * b)) + (y * 0.041666666666666664d0)))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (b <= -1.4e-155) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	} else if (b <= -1.35e-262) {
		tmp = t_2;
	} else if (b <= 8.2e-224) {
		tmp = (x / a) / y;
	} else if (b <= 4.8e-177) {
		tmp = (t_1 - ((t_1 - (x / (a * (y * b)))) / b)) / b;
	} else if (b <= 6.8e+18) {
		tmp = t_2;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if b <= -1.4e-155:
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y
	elif b <= -1.35e-262:
		tmp = t_2
	elif b <= 8.2e-224:
		tmp = (x / a) / y
	elif b <= 4.8e-177:
		tmp = (t_1 - ((t_1 - (x / (a * (y * b)))) / b)) / b
	elif b <= 6.8e+18:
		tmp = t_2
	else:
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (b <= -1.4e-155)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(1.0 / a) * 0.5) - Float64(b * Float64(Float64(Float64(1.0 / a) * 0.16666666666666666) - Float64(Float64(b / a) * 0.041666666666666664))))) + Float64(-1.0 / a))))) / y);
	elseif (b <= -1.35e-262)
		tmp = t_2;
	elseif (b <= 8.2e-224)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4.8e-177)
		tmp = Float64(Float64(t_1 - Float64(Float64(t_1 - Float64(x / Float64(a * Float64(y * b)))) / b)) / b);
	elseif (b <= 6.8e+18)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(b * Float64(Float64(y * 0.16666666666666666) + Float64(b * Float64(Float64(0.008333333333333333 * Float64(y * b)) + Float64(y * 0.041666666666666664))))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (b <= -1.4e-155)
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) - (b * (((1.0 / a) * 0.16666666666666666) - ((b / a) * 0.041666666666666664))))) + (-1.0 / a))))) / y;
	elseif (b <= -1.35e-262)
		tmp = t_2;
	elseif (b <= 8.2e-224)
		tmp = (x / a) / y;
	elseif (b <= 4.8e-177)
		tmp = (t_1 - ((t_1 - (x / (a * (y * b)))) / b)) / b;
	elseif (b <= 6.8e+18)
		tmp = t_2;
	else
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (b * ((0.008333333333333333 * (y * b)) + (y * 0.041666666666666664)))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e-155], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.5), $MachinePrecision] - N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.35e-262], t$95$2, If[LessEqual[b, 8.2e-224], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.8e-177], N[(N[(t$95$1 - N[(N[(t$95$1 - N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, 6.8e+18], t$95$2, N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(b * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(b * N[(N[(0.008333333333333333 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.4e-155

   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 t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. exp-neg 61.0%

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

      2. exp-sum 60.9%

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

      3. rem-exp-log 61.7%

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

      4. associate-/l/ 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in b around 0 56.5%

      \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(b \cdot \left(0.041666666666666664 \cdot \frac{b}{a} - 0.16666666666666666 \cdot \frac{1}{a}\right) + 0.5 \cdot \frac{1}{a}\right) - \frac{1}{a}\right) + \frac{1}{a}\right)}}{y} \]

   if -1.4e-155 < b < -1.3500000000000001e-262 or 4.7999999999999998e-177 < b < 6.8e18

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 63.0%

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

      1. associate-/l* 67.5%

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

      2. div-exp 64.1%

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

      3. exp-to-pow 65.2%

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

      4. sub-neg 65.2%

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

      5. metadata-eval 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 39.7%

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

   7. Taylor expanded in b around 0 40.0%

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

   8. Taylor expanded in b around inf 46.5%

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

      1. associate-/l* 49.9%

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

      2. distribute-lft-out 51.8%

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

   10. Simplified 51.8%

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

   if -1.3500000000000001e-262 < b < 8.19999999999999972e-224

   1. Initial program 94.0%

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

      1. associate-/l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. exp-sum 86.3%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 86.3%

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

      10. sub-neg 86.3%

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

      11. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 83.6%

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

   9. Taylor expanded in y around 0 56.9%

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

   if 8.19999999999999972e-224 < b < 4.7999999999999998e-177

   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 14.8%

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

      1. associate-/l* 14.8%

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

      2. div-exp 14.8%

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

      3. exp-to-pow 14.8%

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

      4. sub-neg 14.8%

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

      5. metadata-eval 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in t around 0 3.4%

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

   7. Taylor expanded in b around 0 3.4%

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

   8. Taylor expanded in b around -inf 39.9%

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

      1. mul-1-neg 39.9%

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

   10. Simplified 39.9%

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

   if 6.8e18 < 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 92.2%

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

      1. associate-/l* 92.2%

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

      2. div-exp 69.9%

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

      3. exp-to-pow 69.9%

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

      4. sub-neg 69.9%

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

      5. metadata-eval 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in t around 0 87.5%

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

   7. Taylor expanded in b around 0 75.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.5 \cdot y + b \cdot \left(0.16666666666666666 \cdot y + b \cdot \left(0.008333333333333333 \cdot \left(b \cdot y\right) + 0.041666666666666664 \cdot y\right)\right)\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-155}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 - b \cdot \left(\frac{1}{a} \cdot 0.16666666666666666 - \frac{b}{a} \cdot 0.041666666666666664\right)\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a} - \frac{\frac{x}{y \cdot a} - \frac{x}{a \cdot \left(y \cdot b\right)}}{b}}{b}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + b \cdot \left(0.008333333333333333 \cdot \left(y \cdot b\right) + y \cdot 0.041666666666666664\right)\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.1% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ t_2 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -8 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 + \frac{b}{a} \cdot -0.16666666666666666\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{t\_2 - \frac{t\_2 - \frac{x}{a \cdot \left(y \cdot b\right)}}{b}}{b}\\ \mathbf{elif}\;b \leq 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))) (t_2 (/ x (* y a))))
   (if (<= b -8e-157)
     (/
      (*
       x
       (+
        (/ 1.0 a)
        (*
         b
         (+
          (* b (+ (* (/ 1.0 a) 0.5) (* (/ b a) -0.16666666666666666)))
          (/ -1.0 a)))))
      y)
     (if (<= b -2.25e-262)
       t_1
       (if (<= b 8.2e-224)
         (/ (/ x a) y)
         (if (<= b 4e-177)
           (/ (- t_2 (/ (- t_2 (/ x (* a (* y b)))) b)) b)
           (if (<= b 1e-61)
             t_1
             (/
              x
              (*
               a
               (*
                y
                (-
                 1.0
                 (*
                  b
                  (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double t_2 = x / (y * a);
	double tmp;
	if (b <= -8e-157) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y;
	} else if (b <= -2.25e-262) {
		tmp = t_1;
	} else if (b <= 8.2e-224) {
		tmp = (x / a) / y;
	} else if (b <= 4e-177) {
		tmp = (t_2 - ((t_2 - (x / (a * (y * b)))) / b)) / b;
	} else if (b <= 1e-61) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (b * (a * (y + (y / b))))
    t_2 = x / (y * a)
    if (b <= (-8d-157)) then
        tmp = (x * ((1.0d0 / a) + (b * ((b * (((1.0d0 / a) * 0.5d0) + ((b / a) * (-0.16666666666666666d0)))) + ((-1.0d0) / a))))) / y
    else if (b <= (-2.25d-262)) then
        tmp = t_1
    else if (b <= 8.2d-224) then
        tmp = (x / a) / y
    else if (b <= 4d-177) then
        tmp = (t_2 - ((t_2 - (x / (a * (y * b)))) / b)) / b
    else if (b <= 1d-61) then
        tmp = t_1
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double t_2 = x / (y * a);
	double tmp;
	if (b <= -8e-157) {
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y;
	} else if (b <= -2.25e-262) {
		tmp = t_1;
	} else if (b <= 8.2e-224) {
		tmp = (x / a) / y;
	} else if (b <= 4e-177) {
		tmp = (t_2 - ((t_2 - (x / (a * (y * b)))) / b)) / b;
	} else if (b <= 1e-61) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	t_2 = x / (y * a)
	tmp = 0
	if b <= -8e-157:
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y
	elif b <= -2.25e-262:
		tmp = t_1
	elif b <= 8.2e-224:
		tmp = (x / a) / y
	elif b <= 4e-177:
		tmp = (t_2 - ((t_2 - (x / (a * (y * b)))) / b)) / b
	elif b <= 1e-61:
		tmp = t_1
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	t_2 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -8e-157)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(b * Float64(Float64(Float64(1.0 / a) * 0.5) + Float64(Float64(b / a) * -0.16666666666666666))) + Float64(-1.0 / a))))) / y);
	elseif (b <= -2.25e-262)
		tmp = t_1;
	elseif (b <= 8.2e-224)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 4e-177)
		tmp = Float64(Float64(t_2 - Float64(Float64(t_2 - Float64(x / Float64(a * Float64(y * b)))) / b)) / b);
	elseif (b <= 1e-61)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	t_2 = x / (y * a);
	tmp = 0.0;
	if (b <= -8e-157)
		tmp = (x * ((1.0 / a) + (b * ((b * (((1.0 / a) * 0.5) + ((b / a) * -0.16666666666666666))) + (-1.0 / a))))) / y;
	elseif (b <= -2.25e-262)
		tmp = t_1;
	elseif (b <= 8.2e-224)
		tmp = (x / a) / y;
	elseif (b <= 4e-177)
		tmp = (t_2 - ((t_2 - (x / (a * (y * b)))) / b)) / b;
	elseif (b <= 1e-61)
		tmp = t_1;
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e-157], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(N[(1.0 / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(N[(b / a), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.25e-262], t$95$1, If[LessEqual[b, 8.2e-224], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4e-177], N[(N[(t$95$2 - N[(N[(t$95$2 - N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[b, 1e-61], t$95$1, N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.99999999999999955e-157

   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 t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. exp-neg 61.0%

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

      2. exp-sum 60.9%

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

      3. rem-exp-log 61.7%

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

      4. associate-/l/ 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in b around 0 54.5%

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

   if -7.99999999999999955e-157 < b < -2.24999999999999999e-262 or 3.99999999999999981e-177 < b < 1e-61

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0 64.5%

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

      1. associate-/l* 69.9%

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

      2. div-exp 69.9%

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

      3. exp-to-pow 71.1%

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

      4. sub-neg 71.1%

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

      5. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around 0 42.7%

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

   7. Taylor expanded in b around 0 42.7%

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

   8. Taylor expanded in b around inf 50.5%

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

      1. associate-/l* 54.6%

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

      2. distribute-lft-out 56.8%

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

   10. Simplified 56.8%

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

   if -2.24999999999999999e-262 < b < 8.19999999999999972e-224

   1. Initial program 94.0%

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

      1. associate-/l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. exp-sum 86.3%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 86.3%

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

      10. sub-neg 86.3%

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

      11. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in b around 0 88.4%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 83.6%

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

   9. Taylor expanded in y around 0 56.9%

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

   if 8.19999999999999972e-224 < b < 3.99999999999999981e-177

   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 14.8%

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

      1. associate-/l* 14.8%

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

      2. div-exp 14.8%

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

      3. exp-to-pow 14.8%

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

      4. sub-neg 14.8%

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

      5. metadata-eval 14.8%

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

   5. Simplified 14.8%

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

   6. Taylor expanded in t around 0 3.4%

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

   7. Taylor expanded in b around 0 3.4%

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

   8. Taylor expanded in b around -inf 39.9%

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

      1. mul-1-neg 39.9%

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

   10. Simplified 39.9%

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

   if 1e-61 < b

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 87.6%

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

      1. associate-/l* 87.5%

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

      2. div-exp 65.4%

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

      3. exp-to-pow 65.5%

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

      4. sub-neg 65.5%

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

      5. metadata-eval 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in t around 0 79.6%

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

   7. Taylor expanded in b around 0 61.1%

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

   8. Taylor expanded in y around 0 66.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(b \cdot \left(\frac{1}{a} \cdot 0.5 + \frac{b}{a} \cdot -0.16666666666666666\right) + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a} - \frac{\frac{x}{y \cdot a} - \frac{x}{a \cdot \left(y \cdot b\right)}}{b}}{b}\\ \mathbf{elif}\;b \leq 10^{-61}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.1% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-258}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + 0.041666666666666664 \cdot \left(y \cdot b\right)\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.6e-258)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* (/ b a) 0.5) (/ -1.0 a))))) y)
   (/
    x
    (*
     a
     (+
      y
      (*
       b
       (+
        y
        (*
         b
         (+
          (* y 0.5)
          (*
           b
           (+
            (* y 0.16666666666666666)
            (* 0.041666666666666664 (* y b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.6e-258) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (0.041666666666666664 * (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 (a <= 1.6d-258) then
        tmp = (x * ((1.0d0 / a) + (b * (((b / a) * 0.5d0) + ((-1.0d0) / a))))) / y
    else
        tmp = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (b * ((y * 0.16666666666666666d0) + (0.041666666666666664d0 * (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 (a <= 1.6e-258) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (0.041666666666666664 * (y * b))))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.6e-258:
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y
	else:
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (0.041666666666666664 * (y * b))))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.6e-258)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(Float64(b / a) * 0.5) + Float64(-1.0 / a))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(b * Float64(Float64(y * 0.16666666666666666) + Float64(0.041666666666666664 * Float64(y * b)))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.6e-258)
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	else
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (b * ((y * 0.16666666666666666) + (0.041666666666666664 * (y * b))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.6e-258], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(b * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(0.041666666666666664 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.6000000000000001e-258

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. exp-neg 63.8%

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

      2. exp-sum 63.8%

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

      3. rem-exp-log 64.4%

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

      4. associate-/l/ 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in b around 0 59.9%

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

   if 1.6000000000000001e-258 < a

   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 y around 0 78.3%

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

      1. associate-/l* 80.2%

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

      2. div-exp 68.2%

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

      3. exp-to-pow 69.2%

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

      4. sub-neg 69.2%

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

      5. metadata-eval 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in t around 0 61.0%

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

   7. Taylor expanded in b around 0 49.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.5 \cdot y + b \cdot \left(0.041666666666666664 \cdot \left(b \cdot y\right) + 0.16666666666666666 \cdot y\right)\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-258}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + b \cdot \left(y \cdot 0.16666666666666666 + 0.041666666666666664 \cdot \left(y \cdot b\right)\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.2% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* b (* a (+ y (/ y b)))))))
   (if (<= y -8.4e+152)
     t_1
     (if (<= y -9.5e-135)
       (/ (* b (- (/ x (* a b)) (/ x a))) y)
       (if (<= y 8.6e-43) (* x (/ 1.0 (* y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (y <= -8.4e+152) {
		tmp = t_1;
	} else if (y <= -9.5e-135) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (y <= 8.6e-43) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (b * (a * (y + (y / b))))
    if (y <= (-8.4d+152)) then
        tmp = t_1
    else if (y <= (-9.5d-135)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else if (y <= 8.6d-43) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (b * (a * (y + (y / b))));
	double tmp;
	if (y <= -8.4e+152) {
		tmp = t_1;
	} else if (y <= -9.5e-135) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (y <= 8.6e-43) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (b * (a * (y + (y / b))))
	tmp = 0
	if y <= -8.4e+152:
		tmp = t_1
	elif y <= -9.5e-135:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	elif y <= 8.6e-43:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))))
	tmp = 0.0
	if (y <= -8.4e+152)
		tmp = t_1;
	elseif (y <= -9.5e-135)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	elseif (y <= 8.6e-43)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (b * (a * (y + (y / b))));
	tmp = 0.0;
	if (y <= -8.4e+152)
		tmp = t_1;
	elseif (y <= -9.5e-135)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	elseif (y <= 8.6e-43)
		tmp = x * (1.0 / (y * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.4e+152], t$95$1, If[LessEqual[y, -9.5e-135], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.6e-43], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4000000000000007e152 or 8.59999999999999927e-43 < 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 y around 0 63.0%

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

      1. associate-/l* 63.9%

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

      2. div-exp 50.2%

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

      3. exp-to-pow 50.2%

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

      4. sub-neg 50.2%

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

      5. metadata-eval 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in t around 0 41.7%

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

   7. Taylor expanded in b around 0 35.6%

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

   8. Taylor expanded in b around inf 35.2%

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

      1. associate-/l* 38.3%

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

      2. distribute-lft-out 42.6%

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

   10. Simplified 42.6%

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

   if -8.4000000000000007e152 < y < -9.50000000000000007e-135

   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 t around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. mul-1-neg 83.7%

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

      3. unsub-neg 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in y around 0 59.3%

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

      1. exp-neg 59.3%

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

      2. exp-sum 59.4%

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

      3. rem-exp-log 60.2%

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

      4. associate-/l/ 60.2%

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

   8. Simplified 60.2%

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

   9. Taylor expanded in b around 0 29.0%

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

   10. Taylor expanded in b around inf 50.1%

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

       1. +-commutative 50.1%

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

       2. mul-1-neg 50.1%

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

       3. unsub-neg 50.1%

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

   12. Simplified 50.1%

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

   if -9.50000000000000007e-135 < y < 8.59999999999999927e-43

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 94.4%

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

      1. associate-/l* 96.2%

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

      2. div-exp 85.0%

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

      3. exp-to-pow 86.8%

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

      4. sub-neg 86.8%

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

      5. metadata-eval 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in b around 0 69.6%

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

      1. exp-to-pow 71.3%

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

      2. sub-neg 71.3%

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

      3. metadata-eval 71.3%

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

   8. Simplified 71.3%

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

   9. Taylor expanded in t around 0 43.7%

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

       1. *-commutative 43.7%

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

   11. Simplified 43.7%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.0% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.4e+152)
   (/ x (* b (* a (+ y (/ y b)))))
   (if (<= y -6.5e-55)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (/ x (* a (+ y (* b (+ y (* 0.5 (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.4e+152) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (y <= -6.5e-55) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (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 (y <= (-7.4d+152)) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (y <= (-6.5d-55)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = x / (a * (y + (b * (y + (0.5d0 * (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 (y <= -7.4e+152) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (y <= -6.5e-55) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.4e+152:
		tmp = x / (b * (a * (y + (y / b))))
	elif y <= -6.5e-55:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.4e+152)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (y <= -6.5e-55)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(0.5 * Float64(y * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.4e+152)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (y <= -6.5e-55)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.4e+152], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-55], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999992e152

   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 40.8%

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

      1. associate-/l* 40.7%

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

      2. div-exp 27.5%

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

      3. exp-to-pow 27.5%

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

      4. sub-neg 27.5%

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

      5. metadata-eval 27.5%

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

   5. Simplified 27.5%

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

   6. Taylor expanded in t around 0 27.9%

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

   7. Taylor expanded in b around 0 45.1%

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

   8. Taylor expanded in b around inf 45.2%

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

      1. associate-/l* 53.6%

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

      2. distribute-lft-out 58.0%

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

   10. Simplified 58.0%

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

   if -7.39999999999999992e152 < y < -6.50000000000000006e-55

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. mul-1-neg 84.0%

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

      3. unsub-neg 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in y around 0 49.1%

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

      1. exp-neg 49.1%

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

      2. exp-sum 49.2%

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

      3. rem-exp-log 49.6%

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

      4. associate-/l/ 49.6%

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

   8. Simplified 49.6%

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

   9. Taylor expanded in b around 0 25.0%

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

   10. Taylor expanded in b around inf 50.7%

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

       1. +-commutative 50.7%

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

       2. mul-1-neg 50.7%

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

       3. unsub-neg 50.7%

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

   12. Simplified 50.7%

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

   if -6.50000000000000006e-55 < y

   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 85.5%

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

      1. associate-/l* 86.9%

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

      2. div-exp 74.8%

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

      3. exp-to-pow 75.9%

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

      4. sub-neg 75.9%

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

      5. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in t around 0 66.1%

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

   7. Taylor expanded in b around 0 42.6%

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

      1. *-commutative 42.6%

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

   9. Simplified 42.6%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.9% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a} \cdot \left(1 - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.2e-258)
   (/ 1.0 (/ y (* (/ x a) (- 1.0 b))))
   (/
    x
    (*
     a
     (* y (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.2e-258) {
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.2d-258) then
        tmp = 1.0d0 / (y / ((x / a) * (1.0d0 - b)))
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.2e-258) {
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.2e-258:
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)))
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.2e-258)
		tmp = Float64(1.0 / Float64(y / Float64(Float64(x / a) * Float64(1.0 - b))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.2e-258)
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)));
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.2e-258], N[(1.0 / N[(y / N[(N[(x / a), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.2000000000000001e-258

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. exp-neg 63.8%

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

      2. exp-sum 63.8%

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

      3. rem-exp-log 64.4%

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

      4. associate-/l/ 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in b around 0 41.6%

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

       1. clear-num 41.7%

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

       2. inv-pow 41.7%

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

       3. fma-define 41.7%

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

       4. associate-/l* 41.6%

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

   11. Applied egg-rr 41.6%

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

       1. unpow-1 41.6%

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

       2. fma-undefine 41.6%

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

       3. associate-*r* 41.6%

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

       4. distribute-lft1-in 50.9%

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

       5. mul-1-neg 50.9%

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

   13. Simplified 50.9%

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

   if 1.2000000000000001e-258 < a

   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 y around 0 78.3%

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

      1. associate-/l* 80.2%

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

      2. div-exp 68.2%

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

      3. exp-to-pow 69.2%

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

      4. sub-neg 69.2%

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

      5. metadata-eval 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in t around 0 61.0%

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

   7. Taylor expanded in b around 0 47.7%

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

   8. Taylor expanded in y around 0 49.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a} \cdot \left(1 - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.5% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.85 \cdot 10^{-257}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2.85e-257)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* (/ b a) 0.5) (/ -1.0 a))))) y)
   (/
    x
    (*
     a
     (* y (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.85e-257) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2.85d-257) then
        tmp = (x * ((1.0d0 / a) + (b * (((b / a) * 0.5d0) + ((-1.0d0) / a))))) / y
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.85e-257) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.85e-257:
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.85e-257)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(Float64(b / a) * 0.5) + Float64(-1.0 / a))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.85e-257)
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.85e-257], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.8499999999999999e-257

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. exp-neg 63.8%

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

      2. exp-sum 63.8%

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

      3. rem-exp-log 64.4%

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

      4. associate-/l/ 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in b around 0 59.9%

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

   if 2.8499999999999999e-257 < a

   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 y around 0 78.3%

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

      1. associate-/l* 80.2%

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

      2. div-exp 68.2%

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

      3. exp-to-pow 69.2%

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

      4. sub-neg 69.2%

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

      5. metadata-eval 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in t around 0 61.0%

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

   7. Taylor expanded in b around 0 47.7%

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

   8. Taylor expanded in y around 0 49.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.85 \cdot 10^{-257}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.26e+34)
   (* b (/ x (* y (- a))))
   (if (<= b 3.5e+61) (* x (/ 1.0 (* y a))) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.26e+34) {
		tmp = b * (x / (y * -a));
	} else if (b <= 3.5e+61) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.26d+34)) then
        tmp = b * (x / (y * -a))
    else if (b <= 3.5d+61) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.26e+34) {
		tmp = b * (x / (y * -a));
	} else if (b <= 3.5e+61) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.26e+34:
		tmp = b * (x / (y * -a))
	elif b <= 3.5e+61:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.26e+34)
		tmp = Float64(b * Float64(x / Float64(y * Float64(-a))));
	elseif (b <= 3.5e+61)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.26e+34)
		tmp = b * (x / (y * -a));
	elseif (b <= 3.5e+61)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.26e+34], N[(b * N[(x / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+61], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2599999999999999e34

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. mul-1-neg 87.7%

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

      3. unsub-neg 87.7%

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

   5. Simplified 87.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 75.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-neg 75.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. exp-sum 75.4%

         \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      3. rem-exp-log 75.4%

         \[\leadsto \frac{x \cdot \frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      4. associate-/l/ 75.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   8. Simplified 75.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 41.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 39.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 39.7%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 43.7%

          \[\leadsto -\color{blue}{b \cdot \frac{x}{a \cdot y}} \]

       3. distribute-rgt-neg-in 43.7%

          \[\leadsto \color{blue}{b \cdot \left(-\frac{x}{a \cdot y}\right)} \]

       4. distribute-frac-neg 43.7%

          \[\leadsto b \cdot \color{blue}{\frac{-x}{a \cdot y}} \]

   12. Simplified 43.7%

       \[\leadsto \color{blue}{b \cdot \frac{-x}{a \cdot y}} \]

   if -1.2599999999999999e34 < b < 3.50000000000000018e61

   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 69.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 70.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 68.3%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in b around 0 66.4%

      \[\leadsto x \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-to-pow 67.8%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 67.8%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 67.8%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

   8. Simplified 67.8%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0 40.1%

      \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 40.1%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot a}} \]

   11. Simplified 40.1%

       \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot a}} \]

   if 3.50000000000000018e61 < 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 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 71.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 71.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 71.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 71.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 71.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 89.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 40.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   8. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   10. Simplified 40.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 40.0% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+16) (* b (/ x (* y (- a)))) (/ x (* b (* a (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+16) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+16)) then
        tmp = b * (x / (y * -a))
    else
        tmp = x / (b * (a * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+16) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+16:
		tmp = b * (x / (y * -a))
	else:
		tmp = x / (b * (a * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+16)
		tmp = Float64(b * Float64(x / Float64(y * Float64(-a))));
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+16)
		tmp = b * (x / (y * -a));
	else
		tmp = x / (b * (a * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+16], N[(b * N[(x / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.25e16

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 86.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 86.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 86.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 86.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 86.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 74.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-neg 74.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. exp-sum 74.9%

         \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      3. rem-exp-log 74.9%

         \[\leadsto \frac{x \cdot \frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      4. associate-/l/ 74.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   8. Simplified 74.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 39.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 37.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 37.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 41.3%

          \[\leadsto -\color{blue}{b \cdot \frac{x}{a \cdot y}} \]

       3. distribute-rgt-neg-in 41.3%

          \[\leadsto \color{blue}{b \cdot \left(-\frac{x}{a \cdot y}\right)} \]

       4. distribute-frac-neg 41.3%

          \[\leadsto b \cdot \color{blue}{\frac{-x}{a \cdot y}} \]

   12. Simplified 41.3%

       \[\leadsto \color{blue}{b \cdot \frac{-x}{a \cdot y}} \]

   if -1.25e16 < b

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 69.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 70.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 70.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 70.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 70.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 56.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 41.6%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   8. Taylor expanded in b around inf 39.0%

      \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-/l* 40.4%

         \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

      2. distribute-lft-out 43.3%

         \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   10. Simplified 43.3%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 36.9% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4.4e-164)
   (/ (* x (- (/ 1.0 a) (/ b a))) y)
   (/ x (* b (* a (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.4e-164) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 4.4d-164) then
        tmp = (x * ((1.0d0 / a) - (b / a))) / y
    else
        tmp = x / (b * (a * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.4e-164) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4.4e-164:
		tmp = (x * ((1.0 / a) - (b / a))) / y
	else:
		tmp = x / (b * (a * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4.4e-164)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4.4e-164)
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	else
		tmp = x / (b * (a * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4.4e-164], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.39999999999999975e-164

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 81.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 81.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 81.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 62.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-neg 62.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. exp-sum 62.4%

         \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      3. rem-exp-log 62.8%

         \[\leadsto \frac{x \cdot \frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      4. associate-/l/ 62.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   8. Simplified 62.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 43.2%

      \[\leadsto \frac{x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 43.2%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)}}{y} \]

       2. mul-1-neg 43.2%

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} + \color{blue}{\left(-\frac{b}{a}\right)}\right)}{y} \]

       3. unsub-neg 43.2%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right)}}{y} \]

   11. Simplified 43.2%

       \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right)}}{y} \]

   if 4.39999999999999975e-164 < a

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 79.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 66.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 67.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 39.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   8. Taylor expanded in b around inf 36.9%

      \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-/l* 38.4%

         \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

      2. distribute-lft-out 40.5%

         \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   10. Simplified 40.5%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{-164}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.5% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{-162}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a} \cdot \left(1 - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.7e-162)
   (/ 1.0 (/ y (* (/ x a) (- 1.0 b))))
   (/ x (* b (* a (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.7e-162) {
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)));
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.7d-162) then
        tmp = 1.0d0 / (y / ((x / a) * (1.0d0 - b)))
    else
        tmp = x / (b * (a * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.7e-162) {
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)));
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.7e-162:
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)))
	else:
		tmp = x / (b * (a * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.7e-162)
		tmp = Float64(1.0 / Float64(y / Float64(Float64(x / a) * Float64(1.0 - b))));
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.7e-162)
		tmp = 1.0 / (y / ((x / a) * (1.0 - b)));
	else
		tmp = x / (b * (a * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.7e-162], N[(1.0 / N[(y / N[(N[(x / a), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.7e-162

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 81.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 81.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 81.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 62.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-neg 62.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. exp-sum 62.4%

         \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      3. rem-exp-log 62.8%

         \[\leadsto \frac{x \cdot \frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      4. associate-/l/ 62.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   8. Simplified 62.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 39.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. clear-num 39.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}} \]

       2. inv-pow 39.7%

          \[\leadsto \color{blue}{{\left(\frac{y}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}\right)}^{-1}} \]

       3. fma-define 39.7%

          \[\leadsto {\left(\frac{y}{\color{blue}{\mathsf{fma}\left(-1, \frac{b \cdot x}{a}, \frac{x}{a}\right)}}\right)}^{-1} \]

       4. associate-/l* 34.7%

          \[\leadsto {\left(\frac{y}{\mathsf{fma}\left(-1, \color{blue}{b \cdot \frac{x}{a}}, \frac{x}{a}\right)}\right)}^{-1} \]

   11. Applied egg-rr 34.7%

       \[\leadsto \color{blue}{{\left(\frac{y}{\mathsf{fma}\left(-1, b \cdot \frac{x}{a}, \frac{x}{a}\right)}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 34.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{\mathsf{fma}\left(-1, b \cdot \frac{x}{a}, \frac{x}{a}\right)}}} \]

       2. fma-undefine 34.7%

          \[\leadsto \frac{1}{\frac{y}{\color{blue}{-1 \cdot \left(b \cdot \frac{x}{a}\right) + \frac{x}{a}}}} \]

       3. associate-*r* 34.7%

          \[\leadsto \frac{1}{\frac{y}{\color{blue}{\left(-1 \cdot b\right) \cdot \frac{x}{a}} + \frac{x}{a}}} \]

       4. distribute-lft1-in 43.2%

          \[\leadsto \frac{1}{\frac{y}{\color{blue}{\left(-1 \cdot b + 1\right) \cdot \frac{x}{a}}}} \]

       5. mul-1-neg 43.2%

          \[\leadsto \frac{1}{\frac{y}{\left(\color{blue}{\left(-b\right)} + 1\right) \cdot \frac{x}{a}}} \]

   13. Simplified 43.2%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{\left(\left(-b\right) + 1\right) \cdot \frac{x}{a}}}} \]

   if 1.7e-162 < a

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 79.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 66.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 67.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 39.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   8. Taylor expanded in b around inf 36.9%

      \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-/l* 38.4%

         \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

      2. distribute-lft-out 40.5%

         \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   10. Simplified 40.5%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.7 \cdot 10^{-162}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a} \cdot \left(1 - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 37.7% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+16) (* b (/ x (* y (- a)))) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+16) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+16)) then
        tmp = b * (x / (y * -a))
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+16) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+16:
		tmp = b * (x / (y * -a))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+16)
		tmp = Float64(b * Float64(x / 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 <= -1.25e+16)
		tmp = b * (x / (y * -a));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+16], N[(b * N[(x / N[(y * (-a)), $MachinePrecision]), $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 < -1.25e16

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 86.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 86.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 86.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 86.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 86.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 74.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-neg 74.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. exp-sum 74.9%

         \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      3. rem-exp-log 74.9%

         \[\leadsto \frac{x \cdot \frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      4. associate-/l/ 74.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   8. Simplified 74.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 39.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 37.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 37.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 41.3%

          \[\leadsto -\color{blue}{b \cdot \frac{x}{a \cdot y}} \]

       3. distribute-rgt-neg-in 41.3%

          \[\leadsto \color{blue}{b \cdot \left(-\frac{x}{a \cdot y}\right)} \]

       4. distribute-frac-neg 41.3%

          \[\leadsto b \cdot \color{blue}{\frac{-x}{a \cdot y}} \]

   12. Simplified 41.3%

       \[\leadsto \color{blue}{b \cdot \frac{-x}{a \cdot y}} \]

   if -1.25e16 < b

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 69.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 70.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 70.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 70.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 70.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 56.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 41.6%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.1% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+127}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e+127) (/ (/ (* 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 <= -1.4e+127) {
		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 <= (-1.4d+127)) 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 <= -1.4e+127) {
		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 <= -1.4e+127:
		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 <= -1.4e+127)
		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 <= -1.4e+127)
		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, -1.4e+127], 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 < -1.4000000000000001e127

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 93.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 93.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 93.0%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 93.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 93.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in y around 0 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{-\left(b + \log a\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-neg 85.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. exp-sum 85.9%

         \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      3. rem-exp-log 85.9%

         \[\leadsto \frac{x \cdot \frac{1}{e^{b} \cdot \color{blue}{a}}}{y} \]

      4. associate-/l/ 85.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   8. Simplified 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 58.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 58.5%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]

   if -1.4000000000000001e127 < b

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 78.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 68.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 69.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 69.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 57.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 39.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+127}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 30.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-154}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1e-154) (/ 1.0 (* y (/ a x))) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e-154) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1d-154) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e-154) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1e-154:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1e-154)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1e-154)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1e-154], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999997e-155

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 80.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 66.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 67.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 56.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 30.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 30.9%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   9. Simplified 30.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   10. Step-by-step derivation

       1. clear-num 31.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. inv-pow 31.2%

          \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

   11. Applied egg-rr 31.2%

       \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 31.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. associate-/l* 32.4%

          \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{a}{x}}} \]

   13. Simplified 32.4%

       \[\leadsto \color{blue}{\frac{1}{y \cdot \frac{a}{x}}} \]

   if 9.9999999999999997e-155 < x

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 79.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 71.0%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 72.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 72.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 72.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in b around 0 57.4%

      \[\leadsto x \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-to-pow 58.4%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 58.4%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 58.4%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

   8. Simplified 58.4%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0 38.7%

      \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 38.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot a}} \]

   11. Simplified 38.7%

       \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{-154}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 35.0% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.6e+61) (* x (/ 1.0 (* y a))) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.6e+61) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.6d+61) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.6e+61) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.6e+61:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.6e+61)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.6e+61)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.6e+61], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.59999999999999973e61

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 67.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 68.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 68.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 68.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 68.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in b around 0 64.2%

      \[\leadsto x \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   7. Step-by-step derivation

      1. exp-to-pow 65.3%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

      2. sub-neg 65.3%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      3. metadata-eval 65.3%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

   8. Simplified 65.3%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t + -1\right)}}}{y} \]

   9. Taylor expanded in t around 0 38.6%

      \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 38.6%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot a}} \]

   11. Simplified 38.6%

       \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot a}} \]

   if 2.59999999999999973e61 < 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 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   4. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 71.5%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 71.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 71.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 71.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 71.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   6. Taylor expanded in t around 0 89.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Taylor expanded in b around 0 40.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   8. Taylor expanded in b around inf 40.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   10. Simplified 40.2%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 30.2% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{1}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (/ 1.0 (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 / (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 * (1.0d0 / (y * a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 / (y * a));
}

Python

def code(x, y, z, t, a, b):
	return x * (1.0 / (y * a))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * Float64(1.0 / Float64(y * a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * (1.0 / (y * a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 79.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
4. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   2. div-exp 68.3%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   3. exp-to-pow 69.2%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   4. sub-neg 69.2%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

   5. metadata-eval 69.2%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

5. Simplified 69.2%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

6. Taylor expanded in b around 0 58.7%

   \[\leadsto x \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
7. Step-by-step derivation

   1. exp-to-pow 59.5%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

   2. sub-neg 59.5%

      \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

   3. metadata-eval 59.5%

      \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

8. Simplified 59.5%

   \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t + -1\right)}}}{y} \]

9. Taylor expanded in t around 0 34.1%

   \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 34.1%

       \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot a}} \]

11. Simplified 34.1%

    \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot a}} \]

12. Final simplification 34.1%

    \[\leadsto x \cdot \frac{1}{y \cdot a} \]
13. Add Preprocessing

Alternative 30: 30.3% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y \cdot a}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ (* y a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / ((y * a) / x);
}

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 = 1.0d0 / ((y * a) / x)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / ((y * a) / x);
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / ((y * a) / x)

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(Float64(y * a) / x))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / ((y * a) / x);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 79.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
4. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   2. div-exp 68.3%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   3. exp-to-pow 69.2%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   4. sub-neg 69.2%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

   5. metadata-eval 69.2%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

5. Simplified 69.2%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

6. Taylor expanded in t around 0 60.2%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

7. Taylor expanded in b around 0 34.0%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
8. Step-by-step derivation

   1. *-commutative 34.0%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

9. Simplified 34.0%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
10. Step-by-step derivation

    1. clear-num 34.2%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

    2. inv-pow 34.2%

       \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

11. Applied egg-rr 34.2%

    \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]
12. Step-by-step derivation

    1. unpow-1 34.2%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

    2. *-commutative 34.2%

       \[\leadsto \frac{1}{\frac{\color{blue}{a \cdot y}}{x}} \]

13. Simplified 34.2%

    \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

14. Final simplification 34.2%

    \[\leadsto \frac{1}{\frac{y \cdot a}{x}} \]
15. Add Preprocessing

Alternative 31: 30.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 79.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
4. Step-by-step derivation

   1. associate-/l* 80.4%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   2. div-exp 68.3%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   3. exp-to-pow 69.2%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   4. sub-neg 69.2%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

   5. metadata-eval 69.2%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

5. Simplified 69.2%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

6. Taylor expanded in t around 0 60.2%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

7. Taylor expanded in b around 0 34.0%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
8. Step-by-step derivation

   1. *-commutative 34.0%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

9. Simplified 34.0%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

10. Final simplification 34.0%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024055 
(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))