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

Percentage Accurate: 98.5% → 98.5%

Time: 25.2s

Alternatives: 23

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + -1\right) \cdot \log a\\ \mathbf{if}\;t_1 \leq -1000000 \lor \neg \left(t_1 \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x \cdot e^{t_1 - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t -1.0) (log a))))
   (if (or (<= t_1 -1000000.0) (not (<= t_1 2e+85)))
     (/ (* x (exp (- t_1 b))) y)
     (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * log(a);
	double tmp;
	if ((t_1 <= -1000000.0) || !(t_1 <= 2e+85)) {
		tmp = (x * exp((t_1 - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + (-1.0d0)) * log(a)
    if ((t_1 <= (-1000000.0d0)) .or. (.not. (t_1 <= 2d+85))) then
        tmp = (x * exp((t_1 - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * Math.log(a);
	double tmp;
	if ((t_1 <= -1000000.0) || !(t_1 <= 2e+85)) {
		tmp = (x * Math.exp((t_1 - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + -1.0) * math.log(a)
	tmp = 0
	if (t_1 <= -1000000.0) or not (t_1 <= 2e+85):
		tmp = (x * math.exp((t_1 - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + -1.0) * log(a))
	tmp = 0.0
	if ((t_1 <= -1000000.0) || !(t_1 <= 2e+85))
		tmp = Float64(Float64(x * exp(Float64(t_1 - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + -1.0) * log(a);
	tmp = 0.0;
	if ((t_1 <= -1000000.0) || ~((t_1 <= 2e+85)))
		tmp = (x * exp((t_1 - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1000000.0], N[Not[LessEqual[t$95$1, 2e+85]], $MachinePrecision]], N[(N[(x * N[Exp[N[(t$95$1 - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t 1) (log.f64 a)) < -1e6 or 2e85 < (*.f64 (-.f64 t 1) (log.f64 a))

   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. Taylor expanded in y around 0 89.1%

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

   if -1e6 < (*.f64 (-.f64 t 1) (log.f64 a)) < 2e85

   1. Initial program 98.6%

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

   2. Taylor expanded in t around 0 96.3%

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

      1. mul-1-neg 96.3%

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

   4. Simplified 96.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t + -1\right) \cdot \log a \leq -1000000 \lor \neg \left(\left(t + -1\right) \cdot \log a \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 88.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+149} \lor \neg \left(y \leq 1.45 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.95e+149) (not (<= y 1.45e+85)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.95e+149) || !(y <= 1.45e+85)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.95d+149)) .or. (.not. (y <= 1.45d+85))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.95e+149) || !(y <= 1.45e+85)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.95e+149) or not (y <= 1.45e+85):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.95e+149) || !(y <= 1.45e+85))
		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 <= -1.95e+149) || ~((y <= 1.45e+85)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.95e+149], N[Not[LessEqual[y, 1.45e+85]], $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 < -1.95e149 or 1.44999999999999999e85 < 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. Taylor expanded in b around 0 97.9%

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

      1. sub-neg 97.9%

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

      2. metadata-eval 97.9%

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

      3. log-pow 90.7%

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

      4. *-commutative 90.7%

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

      5. distribute-rgt-in 90.7%

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

      6. mul-1-neg 90.7%

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

      7. sub-neg 90.7%

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

      8. log-pow 70.5%

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

      9. log-div 70.5%

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

      10. log-prod 70.5%

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

      11. *-commutative 70.5%

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

      12. rem-exp-log 70.5%

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

      13. associate-*l/ 70.5%

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

      14. *-commutative 70.5%

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

      15. associate-/l* 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in t around 0 90.7%

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

   if -1.95e149 < y < 1.44999999999999999e85

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 92.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+149} \lor \neg \left(y \leq 1.45 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 4: 80.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+96} \lor \neg \left(y \leq 5.4 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+96) (not (<= y 5.4e+20)))
   (/ (/ (* x (pow z y)) a) y)
   (* x (/ (pow a t) (* y (* a (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+96) || !(y <= 5.4e+20)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = x * (pow(a, t) / (y * (a * exp(b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.2d+96)) .or. (.not. (y <= 5.4d+20))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = x * ((a ** t) / (y * (a * exp(b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e+96) || !(y <= 5.4e+20)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = x * (Math.pow(a, t) / (y * (a * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e+96) or not (y <= 5.4e+20):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = x * (math.pow(a, t) / (y * (a * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e+96) || !(y <= 5.4e+20))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(x * Float64((a ^ t) / Float64(y * Float64(a * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e+96) || ~((y <= 5.4e+20)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = x * ((a ^ t) / (y * (a * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e+96], N[Not[LessEqual[y, 5.4e+20]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000006e96 or 5.4e20 < 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. Taylor expanded in b around 0 96.6%

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

      1. sub-neg 96.6%

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

      2. metadata-eval 96.6%

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

      3. log-pow 88.2%

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

      4. *-commutative 88.2%

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

      5. distribute-rgt-in 88.2%

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

      6. mul-1-neg 88.2%

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

      7. sub-neg 88.2%

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

      8. log-pow 71.0%

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

      9. log-div 71.0%

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

      10. log-prod 71.0%

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

      11. *-commutative 71.0%

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

      12. rem-exp-log 71.0%

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

      13. associate-*l/ 71.0%

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

      14. *-commutative 71.0%

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

      15. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around 0 88.2%

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

   if -3.20000000000000006e96 < y < 5.4e20

   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. Step-by-step derivation

      1. associate-*r/ 96.7%

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

      2. sub-neg 96.7%

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

      3. exp-sum 82.3%

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

      4. associate-/l* 82.3%

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

      5. associate-/r/ 79.4%

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

      6. exp-neg 79.4%

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

      7. associate-*r/ 79.4%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around 0 82.4%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+96} \lor \neg \left(y \leq 5.4 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]

Alternative 5: 81.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+96} \lor \neg \left(y \leq 5.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.7e+96) (not (<= y 5.5e+21)))
   (/ (/ (* 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 <= -3.7e+96) || !(y <= 5.5e+21)) {
		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 <= (-3.7d+96)) .or. (.not. (y <= 5.5d+21))) 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 <= -3.7e+96) || !(y <= 5.5e+21)) {
		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 <= -3.7e+96) or not (y <= 5.5e+21):
		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 <= -3.7e+96) || !(y <= 5.5e+21))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * 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 <= -3.7e+96) || ~((y <= 5.5e+21)))
		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, -3.7e+96], N[Not[LessEqual[y, 5.5e+21]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999991e96 or 5.5e21 < 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. Taylor expanded in b around 0 96.6%

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

      1. sub-neg 96.6%

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

      2. metadata-eval 96.6%

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

      3. log-pow 88.2%

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

      4. *-commutative 88.2%

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

      5. distribute-rgt-in 88.2%

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

      6. mul-1-neg 88.2%

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

      7. sub-neg 88.2%

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

      8. log-pow 71.0%

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

      9. log-div 71.0%

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

      10. log-prod 71.0%

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

      11. *-commutative 71.0%

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

      12. rem-exp-log 71.0%

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

      13. associate-*l/ 71.0%

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

      14. *-commutative 71.0%

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

      15. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around 0 88.2%

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

   if -3.69999999999999991e96 < y < 5.5e21

   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. Taylor expanded in y around 0 93.7%

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

      1. exp-diff 84.3%

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

      2. sub-neg 84.3%

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

      3. metadata-eval 84.3%

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

      4. *-commutative 84.3%

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

      5. exp-to-pow 84.9%

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

   4. Simplified 84.9%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+96} \lor \neg \left(y \leq 5.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 6: 73.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{a}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ t_3 := x \cdot \frac{t_1}{y}\\ t_4 := y \cdot e^{b}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3450:\\ \;\;\;\;\frac{x}{a \cdot t_4}\\ \mathbf{elif}\;y \leq -2.08 \cdot 10^{-157}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-251}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{a}}{t_4}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow a t) a))
        (t_2 (/ (/ (* x (pow z y)) a) y))
        (t_3 (* x (/ t_1 y)))
        (t_4 (* y (exp b))))
   (if (<= y -1.15e+97)
     t_2
     (if (<= y -8.5e+51)
       t_3
       (if (<= y -2.3e+37)
         (* (/ (pow z y) a) (/ x y))
         (if (<= y -3450.0)
           (/ x (* a t_4))
           (if (<= y -2.08e-157)
             t_3
             (if (<= y 3.7e-302)
               (/ (/ x (* a (exp b))) y)
               (if (<= y 4.4e-251)
                 t_3
                 (if (<= y 1.85e-158)
                   (/ (/ x a) t_4)
                   (if (<= y 1.05e+20) (/ (* x t_1) y) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, t) / a;
	double t_2 = ((x * pow(z, y)) / a) / y;
	double t_3 = x * (t_1 / y);
	double t_4 = y * exp(b);
	double tmp;
	if (y <= -1.15e+97) {
		tmp = t_2;
	} else if (y <= -8.5e+51) {
		tmp = t_3;
	} else if (y <= -2.3e+37) {
		tmp = (pow(z, y) / a) * (x / y);
	} else if (y <= -3450.0) {
		tmp = x / (a * t_4);
	} else if (y <= -2.08e-157) {
		tmp = t_3;
	} else if (y <= 3.7e-302) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 4.4e-251) {
		tmp = t_3;
	} else if (y <= 1.85e-158) {
		tmp = (x / a) / t_4;
	} else if (y <= 1.05e+20) {
		tmp = (x * t_1) / 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (a ** t) / a
    t_2 = ((x * (z ** y)) / a) / y
    t_3 = x * (t_1 / y)
    t_4 = y * exp(b)
    if (y <= (-1.15d+97)) then
        tmp = t_2
    else if (y <= (-8.5d+51)) then
        tmp = t_3
    else if (y <= (-2.3d+37)) then
        tmp = ((z ** y) / a) * (x / y)
    else if (y <= (-3450.0d0)) then
        tmp = x / (a * t_4)
    else if (y <= (-2.08d-157)) then
        tmp = t_3
    else if (y <= 3.7d-302) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 4.4d-251) then
        tmp = t_3
    else if (y <= 1.85d-158) then
        tmp = (x / a) / t_4
    else if (y <= 1.05d+20) then
        tmp = (x * t_1) / 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) / a;
	double t_2 = ((x * Math.pow(z, y)) / a) / y;
	double t_3 = x * (t_1 / y);
	double t_4 = y * Math.exp(b);
	double tmp;
	if (y <= -1.15e+97) {
		tmp = t_2;
	} else if (y <= -8.5e+51) {
		tmp = t_3;
	} else if (y <= -2.3e+37) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else if (y <= -3450.0) {
		tmp = x / (a * t_4);
	} else if (y <= -2.08e-157) {
		tmp = t_3;
	} else if (y <= 3.7e-302) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 4.4e-251) {
		tmp = t_3;
	} else if (y <= 1.85e-158) {
		tmp = (x / a) / t_4;
	} else if (y <= 1.05e+20) {
		tmp = (x * t_1) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, t) / a
	t_2 = ((x * math.pow(z, y)) / a) / y
	t_3 = x * (t_1 / y)
	t_4 = y * math.exp(b)
	tmp = 0
	if y <= -1.15e+97:
		tmp = t_2
	elif y <= -8.5e+51:
		tmp = t_3
	elif y <= -2.3e+37:
		tmp = (math.pow(z, y) / a) * (x / y)
	elif y <= -3450.0:
		tmp = x / (a * t_4)
	elif y <= -2.08e-157:
		tmp = t_3
	elif y <= 3.7e-302:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 4.4e-251:
		tmp = t_3
	elif y <= 1.85e-158:
		tmp = (x / a) / t_4
	elif y <= 1.05e+20:
		tmp = (x * t_1) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((a ^ t) / a)
	t_2 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	t_3 = Float64(x * Float64(t_1 / y))
	t_4 = Float64(y * exp(b))
	tmp = 0.0
	if (y <= -1.15e+97)
		tmp = t_2;
	elseif (y <= -8.5e+51)
		tmp = t_3;
	elseif (y <= -2.3e+37)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	elseif (y <= -3450.0)
		tmp = Float64(x / Float64(a * t_4));
	elseif (y <= -2.08e-157)
		tmp = t_3;
	elseif (y <= 3.7e-302)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 4.4e-251)
		tmp = t_3;
	elseif (y <= 1.85e-158)
		tmp = Float64(Float64(x / a) / t_4);
	elseif (y <= 1.05e+20)
		tmp = Float64(Float64(x * t_1) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a ^ t) / a;
	t_2 = ((x * (z ^ y)) / a) / y;
	t_3 = x * (t_1 / y);
	t_4 = y * exp(b);
	tmp = 0.0;
	if (y <= -1.15e+97)
		tmp = t_2;
	elseif (y <= -8.5e+51)
		tmp = t_3;
	elseif (y <= -2.3e+37)
		tmp = ((z ^ y) / a) * (x / y);
	elseif (y <= -3450.0)
		tmp = x / (a * t_4);
	elseif (y <= -2.08e-157)
		tmp = t_3;
	elseif (y <= 3.7e-302)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 4.4e-251)
		tmp = t_3;
	elseif (y <= 1.85e-158)
		tmp = (x / a) / t_4;
	elseif (y <= 1.05e+20)
		tmp = (x * t_1) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+97], t$95$2, If[LessEqual[y, -8.5e+51], t$95$3, If[LessEqual[y, -2.3e+37], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3450.0], N[(x / N[(a * t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.08e-157], t$95$3, If[LessEqual[y, 3.7e-302], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 4.4e-251], t$95$3, If[LessEqual[y, 1.85e-158], N[(N[(x / a), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[y, 1.05e+20], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.15000000000000003e97 or 1.05e20 < 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. Taylor expanded in b around 0 96.6%

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

      1. sub-neg 96.6%

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

      2. metadata-eval 96.6%

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

      3. log-pow 88.2%

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

      4. *-commutative 88.2%

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

      5. distribute-rgt-in 88.2%

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

      6. mul-1-neg 88.2%

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

      7. sub-neg 88.2%

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

      8. log-pow 71.0%

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

      9. log-div 71.0%

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

      10. log-prod 71.0%

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

      11. *-commutative 71.0%

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

      12. rem-exp-log 71.0%

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

      13. associate-*l/ 71.0%

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

      14. *-commutative 71.0%

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

      15. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around 0 88.2%

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

   if -1.15000000000000003e97 < y < -8.4999999999999999e51 or -3450 < y < -2.08e-157 or 3.7e-302 < y < 4.4e-251

   1. Initial program 97.1%

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

      1. associate-*r/ 98.9%

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

      2. sub-neg 98.9%

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

      3. exp-sum 86.2%

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

      4. associate-/l* 86.2%

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

      5. associate-/r/ 86.2%

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

      6. exp-neg 86.2%

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

      7. associate-*r/ 86.2%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in y around 0 85.2%

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

   5. Taylor expanded in b around 0 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/r* 83.5%

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

   7. Simplified 83.5%

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

   if -8.4999999999999999e51 < y < -2.30000000000000002e37

   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. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 100.0%

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

      1. div-exp 100.0%

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

      2. *-commutative 100.0%

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

      3. exp-to-pow 100.0%

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

      4. rem-exp-log 100.0%

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

      5. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   if -2.30000000000000002e37 < y < -3450

   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-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 37.5%

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

      4. associate-/l* 37.5%

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

      5. associate-/r/ 37.5%

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

      6. exp-neg 37.5%

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

      7. associate-*r/ 37.5%

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

   3. Simplified 12.5%

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

   4. Taylor expanded in y around 0 75.3%

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

   5. Taylor expanded in t around 0 87.8%

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

   if -2.08e-157 < y < 3.7e-302

   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. Taylor expanded in y around 0 99.3%

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

      1. exp-diff 90.3%

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

      2. sub-neg 90.3%

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

      3. metadata-eval 90.3%

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

      4. *-commutative 90.3%

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

      5. exp-to-pow 90.9%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in t around 0 79.6%

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

   if 4.4e-251 < y < 1.85e-158

   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-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 87.5%

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

      5. associate-/r/ 87.5%

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

      6. exp-neg 87.5%

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

      7. associate-*r/ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in y around 0 87.5%

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

   5. Taylor expanded in t around 0 94.0%

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

      1. associate-/r* 94.0%

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

   7. Simplified 94.0%

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

   if 1.85e-158 < y < 1.05e20

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. exp-diff 85.2%

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

      2. sub-neg 85.2%

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

      3. metadata-eval 85.2%

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

      4. *-commutative 85.2%

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

      5. exp-to-pow 86.4%

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

   4. Simplified 86.4%

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

   5. Taylor expanded in b around 0 80.1%

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

   7. Simplified 80.3%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{t}}{a}}}{y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3450:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq -2.08 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 7: 74.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-266}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow a t) a) y))))
   (if (<= t -1.6e+25)
     t_1
     (if (<= t -1.65e-266)
       (* (/ (pow z y) a) (/ x y))
       (if (<= t 3.5e-26) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(a, t) / a) / y);
	double tmp;
	if (t <= -1.6e+25) {
		tmp = t_1;
	} else if (t <= -1.65e-266) {
		tmp = (pow(z, y) / a) * (x / y);
	} else if (t <= 3.5e-26) {
		tmp = (x / (a * exp(b))) / 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 * (((a ** t) / a) / y)
    if (t <= (-1.6d+25)) then
        tmp = t_1
    else if (t <= (-1.65d-266)) then
        tmp = ((z ** y) / a) * (x / y)
    else if (t <= 3.5d-26) then
        tmp = (x / (a * exp(b))) / 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(a, t) / a) / y);
	double tmp;
	if (t <= -1.6e+25) {
		tmp = t_1;
	} else if (t <= -1.65e-266) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else if (t <= 3.5e-26) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(a, t) / a) / y)
	tmp = 0
	if t <= -1.6e+25:
		tmp = t_1
	elif t <= -1.65e-266:
		tmp = (math.pow(z, y) / a) * (x / y)
	elif t <= 3.5e-26:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((a ^ t) / a) / y))
	tmp = 0.0
	if (t <= -1.6e+25)
		tmp = t_1;
	elseif (t <= -1.65e-266)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	elseif (t <= 3.5e-26)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((a ^ t) / a) / y);
	tmp = 0.0;
	if (t <= -1.6e+25)
		tmp = t_1;
	elseif (t <= -1.65e-266)
		tmp = ((z ^ y) / a) * (x / y);
	elseif (t <= 3.5e-26)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+25], t$95$1, If[LessEqual[t, -1.65e-266], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-26], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e25 or 3.49999999999999985e-26 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 99.9%

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

      2. sub-neg 99.9%

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

      3. exp-sum 80.3%

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

      4. associate-/l* 80.3%

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

      5. associate-/r/ 80.3%

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

      6. exp-neg 80.3%

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

      7. associate-*r/ 80.3%

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

   3. Simplified 53.5%

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

   4. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in b around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/r* 79.9%

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

   7. Simplified 79.9%

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

   if -1.6e25 < t < -1.6500000000000001e-266

   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. Taylor expanded in t around 0 96.5%

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

      1. mul-1-neg 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. div-exp 73.8%

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

      2. *-commutative 73.8%

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

      3. exp-to-pow 73.8%

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

      4. rem-exp-log 74.2%

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

      5. associate-*r/ 69.5%

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

   7. Simplified 69.5%

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

   if -1.6500000000000001e-266 < t < 3.49999999999999985e-26

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0 67.8%

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

      1. exp-diff 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. *-commutative 67.8%

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

      5. exp-to-pow 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in t around 0 68.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-266}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 8: 74.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{a}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{t_1}{y}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-266}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow a t) a)))
   (if (<= t -1.3e+25)
     (* x (/ t_1 y))
     (if (<= t -1.7e-266)
       (* (/ (pow z y) a) (/ x y))
       (if (<= t 3.5e-26) (/ (/ x (* a (exp b))) y) (/ (* x t_1) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, t) / a;
	double tmp;
	if (t <= -1.3e+25) {
		tmp = x * (t_1 / y);
	} else if (t <= -1.7e-266) {
		tmp = (pow(z, y) / a) * (x / y);
	} else if (t <= 3.5e-26) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a ** t) / a
    if (t <= (-1.3d+25)) then
        tmp = x * (t_1 / y)
    else if (t <= (-1.7d-266)) then
        tmp = ((z ** y) / a) * (x / y)
    else if (t <= 3.5d-26) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = (x * t_1) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, t) / a;
	double tmp;
	if (t <= -1.3e+25) {
		tmp = x * (t_1 / y);
	} else if (t <= -1.7e-266) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else if (t <= 3.5e-26) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, t) / a
	tmp = 0
	if t <= -1.3e+25:
		tmp = x * (t_1 / y)
	elif t <= -1.7e-266:
		tmp = (math.pow(z, y) / a) * (x / y)
	elif t <= 3.5e-26:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = (x * t_1) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((a ^ t) / a)
	tmp = 0.0
	if (t <= -1.3e+25)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (t <= -1.7e-266)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	elseif (t <= 3.5e-26)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = Float64(Float64(x * t_1) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a ^ t) / a;
	tmp = 0.0;
	if (t <= -1.3e+25)
		tmp = x * (t_1 / y);
	elseif (t <= -1.7e-266)
		tmp = ((z ^ y) / a) * (x / y);
	elseif (t <= 3.5e-26)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = (x * t_1) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -1.3e+25], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-266], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-26], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2999999999999999e25

   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-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 86.4%

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

      4. associate-/l* 86.4%

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

      5. associate-/r/ 86.4%

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

      6. exp-neg 86.4%

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

      7. associate-*r/ 86.4%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in y around 0 74.8%

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

   5. Taylor expanded in b around 0 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/r* 80.0%

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

   7. Simplified 80.0%

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

   if -1.2999999999999999e25 < t < -1.69999999999999997e-266

   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. Taylor expanded in t around 0 96.5%

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

      1. mul-1-neg 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. div-exp 73.8%

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

      2. *-commutative 73.8%

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

      3. exp-to-pow 73.8%

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

      4. rem-exp-log 74.2%

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

      5. associate-*r/ 69.5%

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

   7. Simplified 69.5%

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

   if -1.69999999999999997e-266 < t < 3.49999999999999985e-26

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0 67.8%

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

      1. exp-diff 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. *-commutative 67.8%

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

      5. exp-to-pow 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in t around 0 68.6%

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

   if 3.49999999999999985e-26 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. exp-diff 67.7%

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

      2. sub-neg 67.7%

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

      3. metadata-eval 67.7%

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

      4. *-commutative 67.7%

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

      5. exp-to-pow 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in b around 0 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-266}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 9: 75.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-5} \lor \neg \left(t \leq 3.4 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.5e-5) (not (<= t 3.4e-26)))
   (* x (/ (/ (pow a t) a) y))
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e-5) || !(t <= 3.4e-26)) {
		tmp = x * ((pow(a, t) / a) / y);
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.5d-5)) .or. (.not. (t <= 3.4d-26))) then
        tmp = x * (((a ** t) / a) / y)
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e-5) || !(t <= 3.4e-26)) {
		tmp = x * ((Math.pow(a, t) / a) / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.5e-5) or not (t <= 3.4e-26):
		tmp = x * ((math.pow(a, t) / a) / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.5e-5) || !(t <= 3.4e-26))
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.5e-5) || ~((t <= 3.4e-26)))
		tmp = x * (((a ^ t) / a) / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.5e-5], N[Not[LessEqual[t, 3.4e-26]], $MachinePrecision]], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999934e-5 or 3.40000000000000013e-26 < t

   1. Initial program 99.9%

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

      1. associate-*r/ 99.9%

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

      2. sub-neg 99.9%

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

      3. exp-sum 81.0%

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

      4. associate-/l* 81.0%

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

      5. associate-/r/ 81.0%

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

      6. exp-neg 81.0%

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

      7. associate-*r/ 81.0%

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

   3. Simplified 53.8%

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

   4. Taylor expanded in y around 0 68.4%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-/r* 79.1%

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

   7. Simplified 79.1%

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

   if -7.49999999999999934e-5 < t < 3.40000000000000013e-26

   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. Taylor expanded in y around 0 64.8%

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

      1. exp-diff 64.8%

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

      2. sub-neg 64.8%

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

      3. metadata-eval 64.8%

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

      4. *-commutative 64.8%

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

      5. exp-to-pow 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in t around 0 65.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-5} \lor \neg \left(t \leq 3.4 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 10: 59.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. associate-*r/ 98.2%

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

   2. sub-neg 98.2%

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

   3. exp-sum 80.6%

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

   4. associate-/l* 80.6%

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

   5. associate-/r/ 79.0%

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

   6. exp-neg 79.0%

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

   7. associate-*r/ 79.0%

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

3. Simplified 65.3%

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

4. Taylor expanded in y around 0 65.6%

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

5. Taylor expanded in t around 0 52.6%

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

6. Final simplification 52.6%

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

Alternative 11: 59.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Taylor expanded in y around 0 75.6%

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

   1. exp-diff 67.8%

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

   2. sub-neg 67.8%

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

   3. metadata-eval 67.8%

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

   4. *-commutative 67.8%

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

   5. exp-to-pow 68.1%

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

4. Simplified 68.1%

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

5. Taylor expanded in t around 0 53.0%

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

6. Final simplification 53.0%

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

Alternative 12: 37.6% accurate, 20.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-300} \lor \neg \left(b \leq 7 \cdot 10^{-185}\right) \land b \leq 3.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+168)
   (* (/ x a) (/ (- b) y))
   (if (or (<= b 4e-300) (and (not (<= b 7e-185)) (<= b 3.4e+72)))
     (/ 1.0 (/ a (/ x y)))
     (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+168) {
		tmp = (x / a) * (-b / y);
	} else if ((b <= 4e-300) || (!(b <= 7e-185) && (b <= 3.4e+72))) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+168)) then
        tmp = (x / a) * (-b / y)
    else if ((b <= 4d-300) .or. (.not. (b <= 7d-185)) .and. (b <= 3.4d+72)) then
        tmp = 1.0d0 / (a / (x / y))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+168) {
		tmp = (x / a) * (-b / y);
	} else if ((b <= 4e-300) || (!(b <= 7e-185) && (b <= 3.4e+72))) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+168:
		tmp = (x / a) * (-b / y)
	elif (b <= 4e-300) or (not (b <= 7e-185) and (b <= 3.4e+72)):
		tmp = 1.0 / (a / (x / y))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+168)
		tmp = Float64(Float64(x / a) * Float64(Float64(-b) / y));
	elseif ((b <= 4e-300) || (!(b <= 7e-185) && (b <= 3.4e+72)))
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+168)
		tmp = (x / a) * (-b / y);
	elseif ((b <= 4e-300) || (~((b <= 7e-185)) && (b <= 3.4e+72)))
		tmp = 1.0 / (a / (x / y));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+168], N[(N[(x / a), $MachinePrecision] * N[((-b) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4e-300], And[N[Not[LessEqual[b, 7e-185]], $MachinePrecision], LessEqual[b, 3.4e+72]]], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e168

   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. Taylor expanded in y around 0 100.0%

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

      1. exp-diff 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. *-commutative 73.1%

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

      5. exp-to-pow 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in t around 0 96.2%

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

   6. Taylor expanded in b around 0 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-/l* 59.6%

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

   8. Simplified 59.6%

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

   9. Taylor expanded in b around inf 62.8%

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

       1. mul-1-neg 62.8%

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

       2. times-frac 55.9%

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

   11. Simplified 55.9%

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

   if -1.15e168 < b < 4.0000000000000001e-300 or 6.9999999999999996e-185 < b < 3.3999999999999998e72

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0 89.9%

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

      1. sub-neg 89.9%

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

      2. metadata-eval 89.9%

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

      3. log-pow 80.3%

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

      4. *-commutative 80.3%

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

      5. distribute-rgt-in 80.3%

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

      6. mul-1-neg 80.3%

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

      7. sub-neg 80.3%

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

      8. log-pow 72.1%

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

      9. log-div 72.1%

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

      10. log-prod 72.1%

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

      11. *-commutative 72.1%

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

      12. rem-exp-log 72.6%

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

      13. associate-*l/ 72.6%

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

      14. *-commutative 72.6%

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

      15. associate-/l* 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in t around 0 63.7%

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

   6. Taylor expanded in y around 0 28.6%

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

      1. clear-num 29.3%

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

      2. inv-pow 29.3%

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

      3. *-commutative 29.3%

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

   8. Applied egg-rr 29.3%

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

      1. unpow-1 29.3%

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

      2. associate-/l* 34.1%

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

   10. Simplified 34.1%

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

   if 4.0000000000000001e-300 < b < 6.9999999999999996e-185 or 3.3999999999999998e72 < b

   1. Initial program 100.0%

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

      1. associate-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. associate-/r/ 69.6%

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

      6. exp-neg 69.6%

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

      7. associate-*r/ 69.6%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in y around 0 64.9%

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

   5. Taylor expanded in t around 0 62.0%

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

   6. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. distribute-lft-out 37.1%

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

   8. Simplified 37.1%

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

   9. Taylor expanded in b around -inf 45.5%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-300} \lor \neg \left(b \leq 7 \cdot 10^{-185}\right) \land b \leq 3.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 13: 38.5% accurate, 20.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-193} \lor \neg \left(b \leq 9 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+44)
   (* (/ x y) (- (/ b a)))
   (if (<= b 4.1e-300)
     (/ (/ 1.0 a) (/ y x))
     (if (or (<= b 1.55e-193) (not (<= b 9e+71)))
       (/ x (* y (* a b)))
       (/ 1.0 (/ a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+44) {
		tmp = (x / y) * -(b / a);
	} else if (b <= 4.1e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if ((b <= 1.55e-193) || !(b <= 9e+71)) {
		tmp = x / (y * (a * b));
	} else {
		tmp = 1.0 / (a / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.5d+44)) then
        tmp = (x / y) * -(b / a)
    else if (b <= 4.1d-300) then
        tmp = (1.0d0 / a) / (y / x)
    else if ((b <= 1.55d-193) .or. (.not. (b <= 9d+71))) then
        tmp = x / (y * (a * b))
    else
        tmp = 1.0d0 / (a / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+44) {
		tmp = (x / y) * -(b / a);
	} else if (b <= 4.1e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if ((b <= 1.55e-193) || !(b <= 9e+71)) {
		tmp = x / (y * (a * b));
	} else {
		tmp = 1.0 / (a / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+44:
		tmp = (x / y) * -(b / a)
	elif b <= 4.1e-300:
		tmp = (1.0 / a) / (y / x)
	elif (b <= 1.55e-193) or not (b <= 9e+71):
		tmp = x / (y * (a * b))
	else:
		tmp = 1.0 / (a / (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+44)
		tmp = Float64(Float64(x / y) * Float64(-Float64(b / a)));
	elseif (b <= 4.1e-300)
		tmp = Float64(Float64(1.0 / a) / Float64(y / x));
	elseif ((b <= 1.55e-193) || !(b <= 9e+71))
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+44)
		tmp = (x / y) * -(b / a);
	elseif (b <= 4.1e-300)
		tmp = (1.0 / a) / (y / x);
	elseif ((b <= 1.55e-193) || ~((b <= 9e+71)))
		tmp = x / (y * (a * b));
	else
		tmp = 1.0 / (a / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+44], N[(N[(x / y), $MachinePrecision] * (-N[(b / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 4.1e-300], N[(N[(1.0 / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.55e-193], N[Not[LessEqual[b, 9e+71]], $MachinePrecision]], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.50000000000000027e44

   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. Taylor expanded in y around 0 85.4%

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

      1. exp-diff 72.4%

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

      2. sub-neg 72.4%

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

      3. metadata-eval 72.4%

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

      4. *-commutative 72.4%

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

      5. exp-to-pow 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in t around 0 85.4%

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

   6. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

      5. associate-/l* 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in b around inf 51.9%

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

       1. associate-*r/ 51.9%

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

       2. associate-*r* 51.9%

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

       3. neg-mul-1 51.9%

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

       4. *-commutative 51.9%

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

       5. times-frac 51.9%

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

       6. distribute-frac-neg 51.9%

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

   11. Simplified 51.9%

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

   if -7.50000000000000027e44 < b < 4.1000000000000001e-300

   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. Taylor expanded in y around 0 65.6%

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

      1. associate-/l* 56.5%

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

      2. exp-diff 54.0%

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

      3. sub-neg 54.0%

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

      4. metadata-eval 54.0%

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

      5. *-commutative 54.0%

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

      6. exp-to-pow 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in t around 0 33.8%

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

   6. Taylor expanded in b around 0 31.5%

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

   if 4.1000000000000001e-300 < b < 1.5500000000000001e-193 or 9.00000000000000087e71 < b

   1. Initial program 100.0%

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

      1. associate-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. associate-/r/ 69.6%

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

      6. exp-neg 69.6%

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

      7. associate-*r/ 69.6%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in y around 0 64.9%

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

   5. Taylor expanded in t around 0 62.0%

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

   6. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. distribute-lft-out 37.1%

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

   8. Simplified 37.1%

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

   9. Taylor expanded in b around -inf 45.5%

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

   if 1.5500000000000001e-193 < b < 9.00000000000000087e71

   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. Taylor expanded in b around 0 91.9%

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

      1. sub-neg 91.9%

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

      2. metadata-eval 91.9%

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

      3. log-pow 83.2%

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

      4. *-commutative 83.2%

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

      5. distribute-rgt-in 83.2%

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

      6. mul-1-neg 83.2%

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

      7. sub-neg 83.2%

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

      8. log-pow 80.1%

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

      9. log-div 80.1%

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

      10. log-prod 80.1%

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

      11. *-commutative 80.1%

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

      12. rem-exp-log 80.9%

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

      13. associate-*l/ 80.9%

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

      14. *-commutative 80.9%

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

      15. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 65.5%

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

   6. Taylor expanded in y around 0 27.0%

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

      1. clear-num 28.7%

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

      2. inv-pow 28.7%

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

      3. *-commutative 28.7%

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

   8. Applied egg-rr 28.7%

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

      1. unpow-1 28.7%

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

      2. associate-/l* 32.8%

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

   10. Simplified 32.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-193} \lor \neg \left(b \leq 9 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \end{array} \]

Alternative 14: 38.8% accurate, 20.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot \left(-\frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-182} \lor \neg \left(b \leq 9 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.8e+93)
   (/ (* x (- (/ b a))) y)
   (if (<= b 4.1e-300)
     (/ (/ 1.0 a) (/ y x))
     (if (or (<= b 3.5e-182) (not (<= b 9e+71)))
       (/ x (* y (* a b)))
       (/ 1.0 (/ a (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e+93) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 4.1e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if ((b <= 3.5e-182) || !(b <= 9e+71)) {
		tmp = x / (y * (a * b));
	} else {
		tmp = 1.0 / (a / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.8d+93)) then
        tmp = (x * -(b / a)) / y
    else if (b <= 4.1d-300) then
        tmp = (1.0d0 / a) / (y / x)
    else if ((b <= 3.5d-182) .or. (.not. (b <= 9d+71))) then
        tmp = x / (y * (a * b))
    else
        tmp = 1.0d0 / (a / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.8e+93) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 4.1e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if ((b <= 3.5e-182) || !(b <= 9e+71)) {
		tmp = x / (y * (a * b));
	} else {
		tmp = 1.0 / (a / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.8e+93:
		tmp = (x * -(b / a)) / y
	elif b <= 4.1e-300:
		tmp = (1.0 / a) / (y / x)
	elif (b <= 3.5e-182) or not (b <= 9e+71):
		tmp = x / (y * (a * b))
	else:
		tmp = 1.0 / (a / (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.8e+93)
		tmp = Float64(Float64(x * Float64(-Float64(b / a))) / y);
	elseif (b <= 4.1e-300)
		tmp = Float64(Float64(1.0 / a) / Float64(y / x));
	elseif ((b <= 3.5e-182) || !(b <= 9e+71))
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.8e+93)
		tmp = (x * -(b / a)) / y;
	elseif (b <= 4.1e-300)
		tmp = (1.0 / a) / (y / x);
	elseif ((b <= 3.5e-182) || ~((b <= 9e+71)))
		tmp = x / (y * (a * b));
	else
		tmp = 1.0 / (a / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.8e+93], N[(N[(x * (-N[(b / a), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.1e-300], N[(N[(1.0 / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3.5e-182], N[Not[LessEqual[b, 9e+71]], $MachinePrecision]], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.8000000000000005e93

   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. Taylor expanded in y around 0 88.0%

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

      1. exp-diff 70.9%

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

      2. sub-neg 70.9%

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

      3. metadata-eval 70.9%

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

      4. *-commutative 70.9%

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

      5. exp-to-pow 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in t around 0 85.6%

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

   6. Taylor expanded in b around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-/l* 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in b around inf 53.3%

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

       1. associate-/l* 41.7%

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

       2. associate-/r/ 57.8%

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

       3. associate-*r* 57.8%

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

       4. *-lft-identity 57.8%

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

       5. associate-*l/ 57.8%

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

       6. associate-/r/ 57.8%

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

       7. neg-mul-1 57.8%

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

       8. distribute-lft-neg-in 57.8%

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

       9. *-commutative 57.8%

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

       10. distribute-rgt-neg-in 57.8%

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

       11. neg-mul-1 57.8%

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

       12. associate-/r/ 57.8%

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

       13. associate-*l/ 57.8%

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

       14. *-lft-identity 57.8%

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

       15. mul-1-neg 57.8%

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

   11. Simplified 57.8%

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

   if -7.8000000000000005e93 < b < 4.1000000000000001e-300

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 67.3%

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

      1. associate-/l* 59.5%

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

      2. exp-diff 57.3%

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

      3. sub-neg 57.3%

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

      4. metadata-eval 57.3%

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

      5. *-commutative 57.3%

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

      6. exp-to-pow 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 41.1%

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

   6. Taylor expanded in b around 0 32.9%

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

   if 4.1000000000000001e-300 < b < 3.49999999999999983e-182 or 9.00000000000000087e71 < b

   1. Initial program 100.0%

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

      1. associate-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. associate-/r/ 69.6%

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

      6. exp-neg 69.6%

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

      7. associate-*r/ 69.6%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in y around 0 64.9%

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

   5. Taylor expanded in t around 0 62.0%

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

   6. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. distribute-lft-out 37.1%

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

   8. Simplified 37.1%

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

   9. Taylor expanded in b around -inf 45.5%

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

   if 3.49999999999999983e-182 < b < 9.00000000000000087e71

   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. Taylor expanded in b around 0 91.9%

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

      1. sub-neg 91.9%

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

      2. metadata-eval 91.9%

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

      3. log-pow 83.2%

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

      4. *-commutative 83.2%

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

      5. distribute-rgt-in 83.2%

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

      6. mul-1-neg 83.2%

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

      7. sub-neg 83.2%

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

      8. log-pow 80.1%

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

      9. log-div 80.1%

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

      10. log-prod 80.1%

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

      11. *-commutative 80.1%

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

      12. rem-exp-log 80.9%

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

      13. associate-*l/ 80.9%

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

      14. *-commutative 80.9%

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

      15. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 65.5%

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

   6. Taylor expanded in y around 0 27.0%

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

      1. clear-num 28.7%

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

      2. inv-pow 28.7%

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

      3. *-commutative 28.7%

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

   8. Applied egg-rr 28.7%

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

      1. unpow-1 28.7%

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

      2. associate-/l* 32.8%

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

   10. Simplified 32.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot \left(-\frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-182} \lor \neg \left(b \leq 9 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \end{array} \]

Alternative 15: 39.1% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot \left(-\frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.7e+94)
   (/ (* x (- (/ b a))) y)
   (if (<= b 3.8e-300)
     (/ (/ 1.0 a) (/ y x))
     (if (<= b 1.8e-186) (/ x (* y (* a b))) (/ (/ x (+ a (* a b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e+94) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 3.8e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if (b <= 1.8e-186) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.7d+94)) then
        tmp = (x * -(b / a)) / y
    else if (b <= 3.8d-300) then
        tmp = (1.0d0 / a) / (y / x)
    else if (b <= 1.8d-186) then
        tmp = x / (y * (a * b))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e+94) {
		tmp = (x * -(b / a)) / y;
	} else if (b <= 3.8e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if (b <= 1.8e-186) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.7e+94:
		tmp = (x * -(b / a)) / y
	elif b <= 3.8e-300:
		tmp = (1.0 / a) / (y / x)
	elif b <= 1.8e-186:
		tmp = x / (y * (a * b))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.7e+94)
		tmp = Float64(Float64(x * Float64(-Float64(b / a))) / y);
	elseif (b <= 3.8e-300)
		tmp = Float64(Float64(1.0 / a) / Float64(y / x));
	elseif (b <= 1.8e-186)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.7e+94)
		tmp = (x * -(b / a)) / y;
	elseif (b <= 3.8e-300)
		tmp = (1.0 / a) / (y / x);
	elseif (b <= 1.8e-186)
		tmp = x / (y * (a * b));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.7e+94], N[(N[(x * (-N[(b / a), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.8e-300], N[(N[(1.0 / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-186], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.7000000000000001e94

   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. Taylor expanded in y around 0 88.0%

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

      1. exp-diff 70.9%

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

      2. sub-neg 70.9%

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

      3. metadata-eval 70.9%

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

      4. *-commutative 70.9%

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

      5. exp-to-pow 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in t around 0 85.6%

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

   6. Taylor expanded in b around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-/l* 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in b around inf 53.3%

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

       1. associate-/l* 41.7%

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

       2. associate-/r/ 57.8%

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

       3. associate-*r* 57.8%

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

       4. *-lft-identity 57.8%

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

       5. associate-*l/ 57.8%

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

       6. associate-/r/ 57.8%

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

       7. neg-mul-1 57.8%

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

       8. distribute-lft-neg-in 57.8%

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

       9. *-commutative 57.8%

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

       10. distribute-rgt-neg-in 57.8%

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

       11. neg-mul-1 57.8%

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

       12. associate-/r/ 57.8%

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

       13. associate-*l/ 57.8%

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

       14. *-lft-identity 57.8%

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

       15. mul-1-neg 57.8%

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

   11. Simplified 57.8%

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

   if -1.7000000000000001e94 < b < 3.80000000000000013e-300

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 67.3%

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

      1. associate-/l* 59.5%

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

      2. exp-diff 57.3%

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

      3. sub-neg 57.3%

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

      4. metadata-eval 57.3%

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

      5. *-commutative 57.3%

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

      6. exp-to-pow 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 41.1%

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

   6. Taylor expanded in b around 0 32.9%

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

   if 3.80000000000000013e-300 < b < 1.7999999999999999e-186

   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-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

      6. exp-neg 100.0%

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

      7. associate-*r/ 100.0%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in y around 0 57.8%

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

   5. Taylor expanded in t around 0 22.4%

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

   6. Taylor expanded in b around 0 22.4%

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

      1. +-commutative 22.4%

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

      2. distribute-lft-out 22.4%

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

   8. Simplified 22.4%

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

   9. Taylor expanded in b around -inf 46.1%

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

   if 1.7999999999999999e-186 < b

   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. Taylor expanded in y around 0 78.9%

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

      1. exp-diff 69.6%

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

      2. sub-neg 69.6%

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

      3. metadata-eval 69.6%

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

      4. *-commutative 69.6%

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

      5. exp-to-pow 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in t around 0 56.9%

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

   6. Taylor expanded in b around 0 37.3%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot \left(-\frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 16: 39.1% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+93)
   (/ (- (/ x a) (/ x (/ a b))) y)
   (if (<= b 3.8e-300)
     (/ (/ 1.0 a) (/ y x))
     (if (<= b 2.6e-194) (/ x (* y (* a b))) (/ (/ x (+ a (* a b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+93) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else if (b <= 3.8e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if (b <= 2.6e-194) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.8d+93)) then
        tmp = ((x / a) - (x / (a / b))) / y
    else if (b <= 3.8d-300) then
        tmp = (1.0d0 / a) / (y / x)
    else if (b <= 2.6d-194) then
        tmp = x / (y * (a * b))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+93) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else if (b <= 3.8e-300) {
		tmp = (1.0 / a) / (y / x);
	} else if (b <= 2.6e-194) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+93:
		tmp = ((x / a) - (x / (a / b))) / y
	elif b <= 3.8e-300:
		tmp = (1.0 / a) / (y / x)
	elif b <= 2.6e-194:
		tmp = x / (y * (a * b))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+93)
		tmp = Float64(Float64(Float64(x / a) - Float64(x / Float64(a / b))) / y);
	elseif (b <= 3.8e-300)
		tmp = Float64(Float64(1.0 / a) / Float64(y / x));
	elseif (b <= 2.6e-194)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+93)
		tmp = ((x / a) - (x / (a / b))) / y;
	elseif (b <= 3.8e-300)
		tmp = (1.0 / a) / (y / x);
	elseif (b <= 2.6e-194)
		tmp = x / (y * (a * b));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+93], N[(N[(N[(x / a), $MachinePrecision] - N[(x / N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.8e-300], N[(N[(1.0 / a), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-194], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.8000000000000001e93

   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. Taylor expanded in y around 0 88.0%

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

      1. exp-diff 70.9%

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

      2. sub-neg 70.9%

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

      3. metadata-eval 70.9%

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

      4. *-commutative 70.9%

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

      5. exp-to-pow 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in t around 0 85.6%

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

   6. Taylor expanded in b around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-/l* 57.8%

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

   8. Simplified 57.8%

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

   if -6.8000000000000001e93 < b < 3.80000000000000013e-300

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 67.3%

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

      1. associate-/l* 59.5%

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

      2. exp-diff 57.3%

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

      3. sub-neg 57.3%

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

      4. metadata-eval 57.3%

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

      5. *-commutative 57.3%

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

      6. exp-to-pow 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 41.1%

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

   6. Taylor expanded in b around 0 32.9%

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

   if 3.80000000000000013e-300 < b < 2.60000000000000002e-194

   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-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

      6. exp-neg 100.0%

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

      7. associate-*r/ 100.0%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in y around 0 57.8%

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

   5. Taylor expanded in t around 0 22.4%

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

   6. Taylor expanded in b around 0 22.4%

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

      1. +-commutative 22.4%

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

      2. distribute-lft-out 22.4%

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

   8. Simplified 22.4%

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

   9. Taylor expanded in b around -inf 46.1%

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

   if 2.60000000000000002e-194 < b

   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. Taylor expanded in y around 0 78.9%

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

      1. exp-diff 69.6%

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

      2. sub-neg 69.6%

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

      3. metadata-eval 69.6%

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

      4. *-commutative 69.6%

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

      5. exp-to-pow 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in t around 0 56.9%

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

   6. Taylor expanded in b around 0 37.3%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 17: 34.2% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{-300} \lor \neg \left(b \leq 3.4 \cdot 10^{-185}\right) \land b \leq 7.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b 3.6e-300) (and (not (<= b 3.4e-185)) (<= b 7.6e+71)))
   (/ 1.0 (/ a (/ x y)))
   (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= 3.6e-300) || (!(b <= 3.4e-185) && (b <= 7.6e+71))) {
		tmp = 1.0 / (a / (x / y));
	} 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 <= 3.6d-300) .or. (.not. (b <= 3.4d-185)) .and. (b <= 7.6d+71)) then
        tmp = 1.0d0 / (a / (x / y))
    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 <= 3.6e-300) || (!(b <= 3.4e-185) && (b <= 7.6e+71))) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= 3.6e-300) or (not (b <= 3.4e-185) and (b <= 7.6e+71)):
		tmp = 1.0 / (a / (x / y))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= 3.6e-300) || (!(b <= 3.4e-185) && (b <= 7.6e+71)))
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	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 <= 3.6e-300) || (~((b <= 3.4e-185)) && (b <= 7.6e+71)))
		tmp = 1.0 / (a / (x / y));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, 3.6e-300], And[N[Not[LessEqual[b, 3.4e-185]], $MachinePrecision], LessEqual[b, 7.6e+71]]], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.60000000000000016e-300 or 3.3999999999999998e-185 < b < 7.6000000000000001e71

   1. Initial program 99.0%

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

   2. Taylor expanded in b around 0 85.4%

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

      1. sub-neg 85.4%

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

      2. metadata-eval 85.4%

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

      3. log-pow 75.0%

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

      4. *-commutative 75.0%

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

      5. distribute-rgt-in 75.0%

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

      6. mul-1-neg 75.0%

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

      7. sub-neg 75.0%

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

      8. log-pow 66.8%

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

      9. log-div 66.9%

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

      10. log-prod 66.9%

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

      11. *-commutative 66.9%

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

      12. rem-exp-log 67.3%

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

      13. associate-*l/ 67.3%

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

      14. *-commutative 67.3%

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

      15. associate-/l* 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in t around 0 61.1%

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

   6. Taylor expanded in y around 0 28.7%

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

      1. clear-num 29.2%

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

      2. inv-pow 29.2%

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

      3. *-commutative 29.2%

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

   8. Applied egg-rr 29.2%

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

      1. unpow-1 29.2%

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

      2. associate-/l* 32.5%

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

   10. Simplified 32.5%

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

   if 3.60000000000000016e-300 < b < 3.3999999999999998e-185 or 7.6000000000000001e71 < b

   1. Initial program 100.0%

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

      1. associate-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. associate-/r/ 69.6%

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

      6. exp-neg 69.6%

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

      7. associate-*r/ 69.6%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in y around 0 64.9%

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

   5. Taylor expanded in t around 0 62.0%

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

   6. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. distribute-lft-out 37.1%

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

   8. Simplified 37.1%

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

   9. Taylor expanded in b around inf 42.0%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{-300} \lor \neg \left(b \leq 3.4 \cdot 10^{-185}\right) \land b \leq 7.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 18: 34.7% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{-300} \lor \neg \left(b \leq 3.6 \cdot 10^{-186}\right) \land b \leq 10^{+73}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b 4e-300) (and (not (<= b 3.6e-186)) (<= b 1e+73)))
   (/ 1.0 (/ a (/ x y)))
   (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= 4e-300) || (!(b <= 3.6e-186) && (b <= 1e+73))) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= 4d-300) .or. (.not. (b <= 3.6d-186)) .and. (b <= 1d+73)) then
        tmp = 1.0d0 / (a / (x / y))
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= 4e-300) || (!(b <= 3.6e-186) && (b <= 1e+73))) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= 4e-300) or (not (b <= 3.6e-186) and (b <= 1e+73)):
		tmp = 1.0 / (a / (x / y))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= 4e-300) || (!(b <= 3.6e-186) && (b <= 1e+73)))
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= 4e-300) || (~((b <= 3.6e-186)) && (b <= 1e+73)))
		tmp = 1.0 / (a / (x / y));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, 4e-300], And[N[Not[LessEqual[b, 3.6e-186]], $MachinePrecision], LessEqual[b, 1e+73]]], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.0000000000000001e-300 or 3.5999999999999998e-186 < b < 9.99999999999999983e72

   1. Initial program 99.0%

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

   2. Taylor expanded in b around 0 85.4%

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

      1. sub-neg 85.4%

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

      2. metadata-eval 85.4%

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

      3. log-pow 75.0%

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

      4. *-commutative 75.0%

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

      5. distribute-rgt-in 75.0%

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

      6. mul-1-neg 75.0%

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

      7. sub-neg 75.0%

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

      8. log-pow 66.8%

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

      9. log-div 66.9%

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

      10. log-prod 66.9%

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

      11. *-commutative 66.9%

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

      12. rem-exp-log 67.3%

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

      13. associate-*l/ 67.3%

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

      14. *-commutative 67.3%

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

      15. associate-/l* 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in t around 0 61.1%

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

   6. Taylor expanded in y around 0 28.7%

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

      1. clear-num 29.2%

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

      2. inv-pow 29.2%

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

      3. *-commutative 29.2%

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

   8. Applied egg-rr 29.2%

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

      1. unpow-1 29.2%

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

      2. associate-/l* 32.5%

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

   10. Simplified 32.5%

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

   if 4.0000000000000001e-300 < b < 3.5999999999999998e-186 or 9.99999999999999983e72 < b

   1. Initial program 100.0%

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

      1. associate-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. associate-/r/ 69.6%

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

      6. exp-neg 69.6%

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

      7. associate-*r/ 69.6%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in y around 0 64.9%

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

   5. Taylor expanded in t around 0 62.0%

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

   6. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

      2. distribute-lft-out 37.1%

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

   8. Simplified 37.1%

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

   9. Taylor expanded in b around -inf 45.5%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4 \cdot 10^{-300} \lor \neg \left(b \leq 3.6 \cdot 10^{-186}\right) \land b \leq 10^{+73}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 19: 38.9% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a} - \frac{b}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.6e-300)
   (/ (- (/ 1.0 a) (/ b a)) (/ y x))
   (if (<= b 8.6e-194) (/ x (* y (* a b))) (/ (/ x (+ a (* a b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.6e-300) {
		tmp = ((1.0 / a) - (b / a)) / (y / x);
	} else if (b <= 8.6e-194) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.6d-300) then
        tmp = ((1.0d0 / a) - (b / a)) / (y / x)
    else if (b <= 8.6d-194) then
        tmp = x / (y * (a * b))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.6e-300) {
		tmp = ((1.0 / a) - (b / a)) / (y / x);
	} else if (b <= 8.6e-194) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.6e-300:
		tmp = ((1.0 / a) - (b / a)) / (y / x)
	elif b <= 8.6e-194:
		tmp = x / (y * (a * b))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.6e-300)
		tmp = Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / Float64(y / x));
	elseif (b <= 8.6e-194)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.6e-300)
		tmp = ((1.0 / a) - (b / a)) / (y / x);
	elseif (b <= 8.6e-194)
		tmp = x / (y * (a * b));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.6e-300], N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e-194], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 3.60000000000000016e-300

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 73.7%

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

      1. associate-/l* 66.0%

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

      2. exp-diff 59.2%

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

      3. sub-neg 59.2%

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

      4. metadata-eval 59.2%

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

      5. *-commutative 59.2%

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

      6. exp-to-pow 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in t around 0 52.6%

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

   6. Taylor expanded in b around 0 39.1%

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

      1. mul-1-neg 39.1%

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

   8. Simplified 39.1%

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

   if 3.60000000000000016e-300 < b < 8.60000000000000012e-194

   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-*r/ 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. sub-neg 100.0%

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

      3. exp-sum 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

      6. exp-neg 100.0%

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

      7. associate-*r/ 100.0%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in y around 0 57.8%

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

   5. Taylor expanded in t around 0 22.4%

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

   6. Taylor expanded in b around 0 22.4%

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

      1. +-commutative 22.4%

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

      2. distribute-lft-out 22.4%

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

   8. Simplified 22.4%

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

   9. Taylor expanded in b around -inf 46.1%

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

   if 8.60000000000000012e-194 < b

   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. Taylor expanded in y around 0 78.9%

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

      1. exp-diff 69.6%

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

      2. sub-neg 69.6%

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

      3. metadata-eval 69.6%

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

      4. *-commutative 69.6%

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

      5. exp-to-pow 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in t around 0 56.9%

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

   6. Taylor expanded in b around 0 37.3%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{1}{a} - \frac{b}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 20: 31.7% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.15 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2.15e+171) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.15e+171) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2.15d+171) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.15e+171) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.15e+171:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.15e+171)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.15e+171)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.15e+171], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.15000000000000004e171

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0 85.6%

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

      1. sub-neg 85.6%

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

      2. metadata-eval 85.6%

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

      3. log-pow 76.3%

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

      4. *-commutative 76.3%

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

      5. distribute-rgt-in 76.3%

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

      6. mul-1-neg 76.3%

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

      7. sub-neg 76.3%

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

      8. log-pow 68.2%

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

      9. log-div 68.2%

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

      10. log-prod 68.2%

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

      11. *-commutative 68.2%

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

      12. rem-exp-log 68.5%

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

      13. associate-*l/ 68.5%

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

      14. *-commutative 68.5%

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

      15. associate-/l* 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in t around 0 60.4%

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

   6. Taylor expanded in y around 0 23.8%

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

      1. *-commutative 23.8%

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

      2. associate-/r* 27.2%

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

   8. Simplified 27.2%

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

   if 2.15000000000000004e171 < a

   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. Taylor expanded in b around 0 74.4%

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

      1. sub-neg 74.4%

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

      2. metadata-eval 74.4%

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

      3. log-pow 70.9%

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

      4. *-commutative 70.9%

         \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\log a \cdot \left(t + -1\right)}}}{y} \]

      5. distribute-rgt-in 70.9%

         \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\left(t \cdot \log a + -1 \cdot \log a\right)}}}{y} \]

      6. mul-1-neg 70.9%

         \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \left(t \cdot \log a + \color{blue}{\left(-\log a\right)}\right)}}{y} \]

      7. sub-neg 70.9%

         \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\left(t \cdot \log a - \log a\right)}}}{y} \]

      8. log-pow 61.7%

         \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \left(\color{blue}{\log \left({a}^{t}\right)} - \log a\right)}}{y} \]

      9. log-div 61.7%

         \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}{y} \]

      10. log-prod 61.7%

          \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left({z}^{y} \cdot \frac{{a}^{t}}{a}\right)}}}{y} \]

      11. *-commutative 61.7%

          \[\leadsto \frac{x \cdot e^{\log \color{blue}{\left(\frac{{a}^{t}}{a} \cdot {z}^{y}\right)}}}{y} \]

      12. rem-exp-log 62.2%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{{a}^{t}}{a} \cdot {z}^{y}\right)}}{y} \]

      13. associate-*l/ 62.2%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{t} \cdot {z}^{y}}{a}}}{y} \]

      14. *-commutative 62.2%

          \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y} \cdot {a}^{t}}}{a}}{y} \]

      15. associate-/l* 62.2%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{\frac{a}{{a}^{t}}}}}{y} \]

   4. Simplified 62.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{\frac{a}{{a}^{t}}}}}{y} \]

   5. Taylor expanded in t around 0 57.2%

      \[\leadsto \frac{\color{blue}{\frac{{z}^{y} \cdot x}{a}}}{y} \]

   6. Taylor expanded in y around 0 43.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.15 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 21: 30.6% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{a}{\frac{x}{y}}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ a (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (a / (x / 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 = 1.0d0 / (a / (x / y))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (a / (x / y));
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (a / (x / y))

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(a / Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (a / (x / y));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in b around 0 83.2%

   \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}{y} \]
3. Step-by-step derivation

   1. sub-neg 83.2%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z + \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a}}{y} \]

   2. metadata-eval 83.2%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z + \left(t + \color{blue}{-1}\right) \cdot \log a}}{y} \]

   3. log-pow 75.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left({z}^{y}\right)} + \left(t + -1\right) \cdot \log a}}{y} \]

   4. *-commutative 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\log a \cdot \left(t + -1\right)}}}{y} \]

   5. distribute-rgt-in 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\left(t \cdot \log a + -1 \cdot \log a\right)}}}{y} \]

   6. mul-1-neg 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \left(t \cdot \log a + \color{blue}{\left(-\log a\right)}\right)}}{y} \]

   7. sub-neg 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\left(t \cdot \log a - \log a\right)}}}{y} \]

   8. log-pow 66.8%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \left(\color{blue}{\log \left({a}^{t}\right)} - \log a\right)}}{y} \]

   9. log-div 66.8%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}{y} \]

   10. log-prod 66.8%

       \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left({z}^{y} \cdot \frac{{a}^{t}}{a}\right)}}}{y} \]

   11. *-commutative 66.8%

       \[\leadsto \frac{x \cdot e^{\log \color{blue}{\left(\frac{{a}^{t}}{a} \cdot {z}^{y}\right)}}}{y} \]

   12. rem-exp-log 67.1%

       \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{{a}^{t}}{a} \cdot {z}^{y}\right)}}{y} \]

   13. associate-*l/ 67.1%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{t} \cdot {z}^{y}}{a}}}{y} \]

   14. *-commutative 67.1%

       \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y} \cdot {a}^{t}}}{a}}{y} \]

   15. associate-/l* 67.1%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{\frac{a}{{a}^{t}}}}}{y} \]

4. Simplified 67.1%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{\frac{a}{{a}^{t}}}}}{y} \]

5. Taylor expanded in t around 0 59.7%

   \[\leadsto \frac{\color{blue}{\frac{{z}^{y} \cdot x}{a}}}{y} \]

6. Taylor expanded in y around 0 28.0%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
7. Step-by-step derivation

   1. clear-num 28.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

   2. inv-pow 28.4%

      \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

   3. *-commutative 28.4%

      \[\leadsto {\left(\frac{\color{blue}{a \cdot y}}{x}\right)}^{-1} \]

8. Applied egg-rr 28.4%

   \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
9. Step-by-step derivation

   1. unpow-1 28.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

   2. associate-/l* 29.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{a}{\frac{x}{y}}}} \]

10. Simplified 29.6%

    \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y}}}} \]

11. Final simplification 29.6%

    \[\leadsto \frac{1}{\frac{a}{\frac{x}{y}}} \]

Alternative 22: 30.8% 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 99.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in b around 0 83.2%

   \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}}{y} \]
3. Step-by-step derivation

   1. sub-neg 83.2%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z + \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a}}{y} \]

   2. metadata-eval 83.2%

      \[\leadsto \frac{x \cdot e^{y \cdot \log z + \left(t + \color{blue}{-1}\right) \cdot \log a}}{y} \]

   3. log-pow 75.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left({z}^{y}\right)} + \left(t + -1\right) \cdot \log a}}{y} \]

   4. *-commutative 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\log a \cdot \left(t + -1\right)}}}{y} \]

   5. distribute-rgt-in 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\left(t \cdot \log a + -1 \cdot \log a\right)}}}{y} \]

   6. mul-1-neg 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \left(t \cdot \log a + \color{blue}{\left(-\log a\right)}\right)}}{y} \]

   7. sub-neg 75.1%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\left(t \cdot \log a - \log a\right)}}}{y} \]

   8. log-pow 66.8%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \left(\color{blue}{\log \left({a}^{t}\right)} - \log a\right)}}{y} \]

   9. log-div 66.8%

      \[\leadsto \frac{x \cdot e^{\log \left({z}^{y}\right) + \color{blue}{\log \left(\frac{{a}^{t}}{a}\right)}}}{y} \]

   10. log-prod 66.8%

       \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left({z}^{y} \cdot \frac{{a}^{t}}{a}\right)}}}{y} \]

   11. *-commutative 66.8%

       \[\leadsto \frac{x \cdot e^{\log \color{blue}{\left(\frac{{a}^{t}}{a} \cdot {z}^{y}\right)}}}{y} \]

   12. rem-exp-log 67.1%

       \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{{a}^{t}}{a} \cdot {z}^{y}\right)}}{y} \]

   13. associate-*l/ 67.1%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{t} \cdot {z}^{y}}{a}}}{y} \]

   14. *-commutative 67.1%

       \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y} \cdot {a}^{t}}}{a}}{y} \]

   15. associate-/l* 67.1%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{\frac{a}{{a}^{t}}}}}{y} \]

4. Simplified 67.1%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{\frac{a}{{a}^{t}}}}}{y} \]

5. Taylor expanded in t around 0 59.7%

   \[\leadsto \frac{\color{blue}{\frac{{z}^{y} \cdot x}{a}}}{y} \]

6. Taylor expanded in y around 0 28.0%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

7. Final simplification 28.0%

   \[\leadsto \frac{x}{y \cdot a} \]

Alternative 23: 30.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x y) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / y) / a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / y) / a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / y) / a;
}

Python

def code(x, y, z, t, a, b):
	return (x / y) / a

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / y) / a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / y) / a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in y around 0 75.6%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]
3. Step-by-step derivation

   1. exp-diff 67.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

   2. sub-neg 67.8%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a}}{e^{b}}}{y} \]

   3. metadata-eval 67.8%

      \[\leadsto \frac{x \cdot \frac{e^{\left(t + \color{blue}{-1}\right) \cdot \log a}}{e^{b}}}{y} \]

   4. *-commutative 67.8%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log a \cdot \left(t + -1\right)}}}{e^{b}}}{y} \]

   5. exp-to-pow 68.1%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t + -1\right)}}}{e^{b}}}{y} \]

4. Simplified 68.1%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

5. Taylor expanded in b around 0 58.0%

   \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)} \cdot x}}{y} \]

7. Simplified 58.0%

   \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{t}}{a}}}{y} \]

8. Taylor expanded in t around 0 28.0%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
9. Step-by-step derivation

   1. associate-/r* 29.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

10. Simplified 29.3%

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

11. Final simplification 29.3%

    \[\leadsto \frac{\frac{x}{y}}{a} \]

Developer target: 72.2% 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 2023257 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (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))