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

Percentage Accurate: 98.3% → 98.3%

Time: 25.0s

Alternatives: 27

Speedup: 1.0×

• 47.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

3. Final simplification 98.5%

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

Alternative 2: 93.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+34} \lor \neg \left(t + -1 \leq 8000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+34) (not (<= (+ t -1.0) 8000000.0)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+34) || !((t + -1.0) <= 8000000.0)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+34)) .or. (.not. ((t + (-1.0d0)) <= 8000000.0d0))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+34) || !((t + -1.0) <= 8000000.0)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+34) or not ((t + -1.0) <= 8000000.0):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+34) || !(Float64(t + -1.0) <= 8000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+34) || ~(((t + -1.0) <= 8000000.0)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+34], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 8000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -9.99999999999999946e33 or 8e6 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.9%

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

   if -9.99999999999999946e33 < (-.f64 t #s(literal 1 binary64)) < 8e6

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 97.4%

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

      1. +-commutative 97.4%

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

      2. mul-1-neg 97.4%

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

      3. unsub-neg 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+34} \lor \neg \left(t + -1 \leq 8000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;y \leq -6000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-195}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-240}:\\ \;\;\;\;x \cdot t\_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{t\_2}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))) (t_2 (/ (pow a (+ t -1.0)) y)))
   (if (<= y -6000000.0)
     t_1
     (if (<= y -1.15e-195)
       (/ (/ x (* a (exp b))) y)
       (if (<= y 8.8e-240)
         (* x t_2)
         (if (<= y 3.4e+49) (* x (/ t_2 (exp b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(z, y) / a) / y);
	double t_2 = pow(a, (t + -1.0)) / y;
	double tmp;
	if (y <= -6000000.0) {
		tmp = t_1;
	} else if (y <= -1.15e-195) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 8.8e-240) {
		tmp = x * t_2;
	} else if (y <= 3.4e+49) {
		tmp = x * (t_2 / exp(b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((z ** y) / a) / y)
    t_2 = (a ** (t + (-1.0d0))) / y
    if (y <= (-6000000.0d0)) then
        tmp = t_1
    else if (y <= (-1.15d-195)) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 8.8d-240) then
        tmp = x * t_2
    else if (y <= 3.4d+49) then
        tmp = x * (t_2 / exp(b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((Math.pow(z, y) / a) / y);
	double t_2 = Math.pow(a, (t + -1.0)) / y;
	double tmp;
	if (y <= -6000000.0) {
		tmp = t_1;
	} else if (y <= -1.15e-195) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 8.8e-240) {
		tmp = x * t_2;
	} else if (y <= 3.4e+49) {
		tmp = x * (t_2 / Math.exp(b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(z, y) / a) / y)
	t_2 = math.pow(a, (t + -1.0)) / y
	tmp = 0
	if y <= -6000000.0:
		tmp = t_1
	elif y <= -1.15e-195:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 8.8e-240:
		tmp = x * t_2
	elif y <= 3.4e+49:
		tmp = x * (t_2 / math.exp(b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	t_2 = Float64((a ^ Float64(t + -1.0)) / y)
	tmp = 0.0
	if (y <= -6000000.0)
		tmp = t_1;
	elseif (y <= -1.15e-195)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 8.8e-240)
		tmp = Float64(x * t_2);
	elseif (y <= 3.4e+49)
		tmp = Float64(x * Float64(t_2 / exp(b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((z ^ y) / a) / y);
	t_2 = (a ^ (t + -1.0)) / y;
	tmp = 0.0;
	if (y <= -6000000.0)
		tmp = t_1;
	elseif (y <= -1.15e-195)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 8.8e-240)
		tmp = x * t_2;
	elseif (y <= 3.4e+49)
		tmp = x * (t_2 / exp(b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -6000000.0], t$95$1, If[LessEqual[y, -1.15e-195], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.8e-240], N[(x * t$95$2), $MachinePrecision], If[LessEqual[y, 3.4e+49], N[(x * N[(t$95$2 / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6e6 or 3.4000000000000001e49 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. mul-1-neg 93.1%

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

      3. unsub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in b around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. div-exp 82.7%

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

      3. *-commutative 82.7%

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

      4. exp-to-pow 82.7%

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

      5. rem-exp-log 82.7%

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

   8. Simplified 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 82.7%

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

   10. Applied egg-rr 82.7%

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

   if -6e6 < y < -1.1500000000000001e-195

   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. Add Preprocessing

   3. Taylor expanded in y around 0 98.4%

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

      1. div-exp 86.7%

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

      2. exp-to-pow 88.1%

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

      3. sub-neg 88.1%

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

      4. metadata-eval 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around 0 82.8%

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

   if -1.1500000000000001e-195 < y < 8.7999999999999997e-240

   1. Initial program 95.8%

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

      1. associate-/l* 93.6%

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

      2. associate--l+ 93.6%

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

      3. exp-sum 93.6%

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

      4. associate-/l* 93.6%

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

      5. *-commutative 93.6%

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

      6. exp-to-pow 93.6%

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

      7. exp-diff 76.9%

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

      8. *-commutative 76.9%

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

      9. exp-to-pow 77.9%

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

      10. sub-neg 77.9%

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

      11. metadata-eval 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in y around 0 76.9%

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

      1. associate-/r* 74.2%

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

      2. exp-to-pow 75.2%

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

      3. sub-neg 75.2%

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

      4. metadata-eval 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in b around 0 86.2%

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

   10. Simplified 87.0%

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

   if 8.7999999999999997e-240 < y < 3.4000000000000001e49

   1. Initial program 97.5%

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

      1. associate-/l* 96.3%

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

      2. associate--l+ 96.3%

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

      3. exp-sum 89.4%

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

      4. associate-/l* 89.4%

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

      5. *-commutative 89.4%

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

      6. exp-to-pow 89.4%

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

      7. exp-diff 79.7%

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

      8. *-commutative 79.7%

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

      9. exp-to-pow 80.6%

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

      10. sub-neg 80.6%

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

      11. metadata-eval 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in y around 0 82.0%

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

      1. associate-/r* 82.0%

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

      2. exp-to-pow 82.8%

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

      3. sub-neg 82.8%

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

      4. metadata-eval 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6000000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-195}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -6500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -6500000.0)
     t_1
     (if (<= y -8e-68)
       (/ x (* a (* y (exp b))))
       (if (<= y 3.8e+49) (/ (* x (/ (pow a (+ t -1.0)) (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(z, y) / a) / y);
	double tmp;
	if (y <= -6500000.0) {
		tmp = t_1;
	} else if (y <= -8e-68) {
		tmp = x / (a * (y * exp(b)));
	} else if (y <= 3.8e+49) {
		tmp = (x * (pow(a, (t + -1.0)) / 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 * (((z ** y) / a) / y)
    if (y <= (-6500000.0d0)) then
        tmp = t_1
    else if (y <= (-8d-68)) then
        tmp = x / (a * (y * exp(b)))
    else if (y <= 3.8d+49) then
        tmp = (x * ((a ** (t + (-1.0d0))) / 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(z, y) / a) / y);
	double tmp;
	if (y <= -6500000.0) {
		tmp = t_1;
	} else if (y <= -8e-68) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (y <= 3.8e+49) {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(z, y) / a) / y)
	tmp = 0
	if y <= -6500000.0:
		tmp = t_1
	elif y <= -8e-68:
		tmp = x / (a * (y * math.exp(b)))
	elif y <= 3.8e+49:
		tmp = (x * (math.pow(a, (t + -1.0)) / 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((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -6500000.0)
		tmp = t_1;
	elseif (y <= -8e-68)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (y <= 3.8e+49)
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / 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 * (((z ^ y) / a) / y);
	tmp = 0.0;
	if (y <= -6500000.0)
		tmp = t_1;
	elseif (y <= -8e-68)
		tmp = x / (a * (y * exp(b)));
	elseif (y <= 3.8e+49)
		tmp = (x * ((a ^ (t + -1.0)) / 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[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6500000.0], t$95$1, If[LessEqual[y, -8e-68], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+49], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e6 or 3.7999999999999999e49 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. mul-1-neg 93.1%

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

      3. unsub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in b around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. div-exp 82.7%

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

      3. *-commutative 82.7%

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

      4. exp-to-pow 82.7%

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

      5. rem-exp-log 82.7%

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

   8. Simplified 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 82.7%

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

   10. Applied egg-rr 82.7%

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

   if -6.5e6 < y < -8.00000000000000053e-68

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 90.6%

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

      4. associate-/l* 90.6%

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

      5. *-commutative 90.6%

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

      6. exp-to-pow 90.6%

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

      7. exp-diff 67.5%

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

      8. *-commutative 67.5%

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

      9. exp-to-pow 69.1%

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

      10. sub-neg 69.1%

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

      11. metadata-eval 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. associate-/r* 67.5%

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

      2. exp-to-pow 69.1%

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

      3. sub-neg 69.1%

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

      4. metadata-eval 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in t around 0 100.0%

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

   if -8.00000000000000053e-68 < y < 3.7999999999999999e49

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0 95.4%

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

      1. div-exp 84.5%

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

      2. exp-to-pow 85.8%

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

      3. sub-neg 85.8%

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

      4. metadata-eval 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6500000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+148} \lor \neg \left(y \leq 3.6 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.1e+148) (not (<= y 3.6e+105)))
   (* 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 <= -5.1e+148) || !(y <= 3.6e+105)) {
		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 <= (-5.1d+148)) .or. (.not. (y <= 3.6d+105))) 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 <= -5.1e+148) || !(y <= 3.6e+105)) {
		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 <= -5.1e+148) or not (y <= 3.6e+105):
		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 <= -5.1e+148) || !(y <= 3.6e+105))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.1e+148) || ~((y <= 3.6e+105)))
		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, -5.1e+148], N[Not[LessEqual[y, 3.6e+105]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.09999999999999985e148 or 3.5999999999999999e105 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around 0 89.6%

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

      1. *-commutative 89.6%

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

      2. div-exp 89.6%

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

      3. *-commutative 89.6%

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

      4. exp-to-pow 89.6%

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

      5. rem-exp-log 89.6%

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

   8. Simplified 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-/l* 89.6%

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

   10. Applied egg-rr 89.6%

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

   if -5.09999999999999985e148 < y < 3.5999999999999999e105

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 91.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+148} \lor \neg \left(y \leq 3.6 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{{z}^{y}}{a}\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-202}:\\ \;\;\;\;t\_2 \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t\_2}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))) (t_2 (/ (pow z y) a)))
   (if (<= b -1.45e+107)
     t_1
     (if (<= b -5.5e-122)
       (* x (/ (pow a (+ t -1.0)) y))
       (if (<= b -3e-202)
         (* t_2 (/ x y))
         (if (<= b 9.5e+30) (* x (/ t_2 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = pow(z, y) / a;
	double tmp;
	if (b <= -1.45e+107) {
		tmp = t_1;
	} else if (b <= -5.5e-122) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else if (b <= -3e-202) {
		tmp = t_2 * (x / y);
	} else if (b <= 9.5e+30) {
		tmp = x * (t_2 / 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) :: t_2
    real(8) :: tmp
    t_1 = x / (a * (y * exp(b)))
    t_2 = (z ** y) / a
    if (b <= (-1.45d+107)) then
        tmp = t_1
    else if (b <= (-5.5d-122)) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else if (b <= (-3d-202)) then
        tmp = t_2 * (x / y)
    else if (b <= 9.5d+30) then
        tmp = x * (t_2 / 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 / (a * (y * Math.exp(b)));
	double t_2 = Math.pow(z, y) / a;
	double tmp;
	if (b <= -1.45e+107) {
		tmp = t_1;
	} else if (b <= -5.5e-122) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else if (b <= -3e-202) {
		tmp = t_2 * (x / y);
	} else if (b <= 9.5e+30) {
		tmp = x * (t_2 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = math.pow(z, y) / a
	tmp = 0
	if b <= -1.45e+107:
		tmp = t_1
	elif b <= -5.5e-122:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	elif b <= -3e-202:
		tmp = t_2 * (x / y)
	elif b <= 9.5e+30:
		tmp = x * (t_2 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64((z ^ y) / a)
	tmp = 0.0
	if (b <= -1.45e+107)
		tmp = t_1;
	elseif (b <= -5.5e-122)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	elseif (b <= -3e-202)
		tmp = Float64(t_2 * Float64(x / y));
	elseif (b <= 9.5e+30)
		tmp = Float64(x * Float64(t_2 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = (z ^ y) / a;
	tmp = 0.0;
	if (b <= -1.45e+107)
		tmp = t_1;
	elseif (b <= -5.5e-122)
		tmp = x * ((a ^ (t + -1.0)) / y);
	elseif (b <= -3e-202)
		tmp = t_2 * (x / y);
	elseif (b <= 9.5e+30)
		tmp = x * (t_2 / 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[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b, -1.45e+107], t$95$1, If[LessEqual[b, -5.5e-122], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-202], N[(t$95$2 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+30], N[(x * N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.44999999999999994e107 or 9.5000000000000003e30 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 76.1%

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

      4. associate-/l* 76.1%

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

      5. *-commutative 76.1%

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

      6. exp-to-pow 76.1%

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

      7. exp-diff 58.7%

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

      8. *-commutative 58.7%

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

      9. exp-to-pow 58.7%

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

      10. sub-neg 58.7%

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

      11. metadata-eval 58.7%

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

   3. Simplified 58.7%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. associate-/r* 66.4%

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

      2. exp-to-pow 66.4%

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

      3. sub-neg 66.4%

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

      4. metadata-eval 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in t around 0 86.1%

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

   if -1.44999999999999994e107 < b < -5.50000000000000053e-122

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

      3. exp-sum 76.2%

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

      4. associate-/l* 76.2%

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

      5. *-commutative 76.2%

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

      6. exp-to-pow 76.2%

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

      7. exp-diff 70.3%

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

      8. *-commutative 70.3%

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

      9. exp-to-pow 70.6%

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

      10. sub-neg 70.6%

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

      11. metadata-eval 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 68.7%

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

      1. associate-/r* 66.7%

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

      2. exp-to-pow 66.9%

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

      3. sub-neg 66.9%

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

      4. metadata-eval 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in b around 0 73.1%

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

   10. Simplified 73.3%

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

   if -5.50000000000000053e-122 < b < -3.00000000000000011e-202

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in b around 0 75.3%

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

      1. div-exp 75.2%

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

      2. *-commutative 75.2%

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

      3. exp-to-pow 75.2%

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

      4. rem-exp-log 78.1%

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

      5. associate-/l* 78.1%

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

      6. associate-/r* 72.9%

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

      7. *-commutative 72.9%

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

      8. times-frac 83.3%

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

   8. Simplified 83.3%

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

   if -3.00000000000000011e-202 < b < 9.5000000000000003e30

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. mul-1-neg 84.4%

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

      3. unsub-neg 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in b around 0 83.7%

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

      1. *-commutative 83.7%

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

      2. div-exp 83.7%

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

      3. *-commutative 83.7%

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

      4. exp-to-pow 83.7%

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

      5. rem-exp-log 84.9%

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

   8. Simplified 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-/l* 82.8%

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

   10. Applied egg-rr 82.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-202}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{{z}^{y}}{a}\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-231}:\\ \;\;\;\;t\_2 \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot t\_2}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))) (t_2 (/ (pow z y) a)))
   (if (<= b -1.45e+107)
     t_1
     (if (<= b -1.95e-120)
       (* x (/ (pow a (+ t -1.0)) y))
       (if (<= b -5e-231)
         (* t_2 (/ x y))
         (if (<= b 4.9e+33) (/ (* x t_2) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = pow(z, y) / a;
	double tmp;
	if (b <= -1.45e+107) {
		tmp = t_1;
	} else if (b <= -1.95e-120) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else if (b <= -5e-231) {
		tmp = t_2 * (x / y);
	} else if (b <= 4.9e+33) {
		tmp = (x * t_2) / 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) :: t_2
    real(8) :: tmp
    t_1 = x / (a * (y * exp(b)))
    t_2 = (z ** y) / a
    if (b <= (-1.45d+107)) then
        tmp = t_1
    else if (b <= (-1.95d-120)) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else if (b <= (-5d-231)) then
        tmp = t_2 * (x / y)
    else if (b <= 4.9d+33) then
        tmp = (x * t_2) / 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 / (a * (y * Math.exp(b)));
	double t_2 = Math.pow(z, y) / a;
	double tmp;
	if (b <= -1.45e+107) {
		tmp = t_1;
	} else if (b <= -1.95e-120) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else if (b <= -5e-231) {
		tmp = t_2 * (x / y);
	} else if (b <= 4.9e+33) {
		tmp = (x * t_2) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = math.pow(z, y) / a
	tmp = 0
	if b <= -1.45e+107:
		tmp = t_1
	elif b <= -1.95e-120:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	elif b <= -5e-231:
		tmp = t_2 * (x / y)
	elif b <= 4.9e+33:
		tmp = (x * t_2) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64((z ^ y) / a)
	tmp = 0.0
	if (b <= -1.45e+107)
		tmp = t_1;
	elseif (b <= -1.95e-120)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	elseif (b <= -5e-231)
		tmp = Float64(t_2 * Float64(x / y));
	elseif (b <= 4.9e+33)
		tmp = Float64(Float64(x * t_2) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = (z ^ y) / a;
	tmp = 0.0;
	if (b <= -1.45e+107)
		tmp = t_1;
	elseif (b <= -1.95e-120)
		tmp = x * ((a ^ (t + -1.0)) / y);
	elseif (b <= -5e-231)
		tmp = t_2 * (x / y);
	elseif (b <= 4.9e+33)
		tmp = (x * t_2) / 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[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b, -1.45e+107], t$95$1, If[LessEqual[b, -1.95e-120], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5e-231], N[(t$95$2 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.9e+33], N[(N[(x * t$95$2), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.44999999999999994e107 or 4.90000000000000014e33 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 76.1%

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

      4. associate-/l* 76.1%

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

      5. *-commutative 76.1%

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

      6. exp-to-pow 76.1%

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

      7. exp-diff 58.7%

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

      8. *-commutative 58.7%

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

      9. exp-to-pow 58.7%

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

      10. sub-neg 58.7%

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

      11. metadata-eval 58.7%

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

   3. Simplified 58.7%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. associate-/r* 66.4%

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

      2. exp-to-pow 66.4%

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

      3. sub-neg 66.4%

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

      4. metadata-eval 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in t around 0 86.1%

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

   if -1.44999999999999994e107 < b < -1.9500000000000001e-120

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

      3. exp-sum 76.2%

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

      4. associate-/l* 76.2%

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

      5. *-commutative 76.2%

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

      6. exp-to-pow 76.2%

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

      7. exp-diff 70.3%

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

      8. *-commutative 70.3%

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

      9. exp-to-pow 70.6%

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

      10. sub-neg 70.6%

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

      11. metadata-eval 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 68.7%

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

      1. associate-/r* 66.7%

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

      2. exp-to-pow 66.9%

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

      3. sub-neg 66.9%

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

      4. metadata-eval 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in b around 0 73.1%

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

   10. Simplified 73.3%

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

   if -1.9500000000000001e-120 < b < -5.00000000000000023e-231

   1. Initial program 93.2%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in b around 0 75.3%

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

      1. div-exp 75.2%

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

      2. *-commutative 75.2%

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

      3. exp-to-pow 75.2%

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

      4. rem-exp-log 77.6%

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

      5. associate-/l* 77.6%

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

      6. associate-/r* 73.4%

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

      7. *-commutative 73.4%

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

      8. times-frac 81.9%

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

   8. Simplified 81.9%

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

   if -5.00000000000000023e-231 < b < 4.90000000000000014e33

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. mul-1-neg 84.8%

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

      3. unsub-neg 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in b around 0 84.1%

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

      1. *-commutative 84.1%

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

      2. div-exp 84.1%

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

      3. *-commutative 84.1%

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

      4. exp-to-pow 84.1%

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

      5. rem-exp-log 85.3%

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

   8. Simplified 85.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-231}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+99} \lor \neg \left(b \leq 7.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+99) (not (<= b 7.2e+27)))
   (/ x (* a (* y (exp b))))
   (* x (/ (/ (pow z y) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+99) || !(b <= 7.2e+27)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * ((pow(z, y) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.5d+99)) .or. (.not. (b <= 7.2d+27))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (((z ** y) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+99) || !(b <= 7.2e+27)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e+99) or not (b <= 7.2e+27):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e+99) || !(b <= 7.2e+27))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e+99) || ~((b <= 7.2e+27)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e+99], N[Not[LessEqual[b, 7.2e+27]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4999999999999998e99 or 7.19999999999999966e27 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 76.8%

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

      4. associate-/l* 76.8%

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

      5. *-commutative 76.8%

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

      6. exp-to-pow 76.8%

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

      7. exp-diff 58.9%

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

      8. *-commutative 58.9%

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

      9. exp-to-pow 58.9%

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

      10. sub-neg 58.9%

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

      11. metadata-eval 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. associate-/r* 66.4%

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

      2. exp-to-pow 66.4%

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

      3. sub-neg 66.4%

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

      4. metadata-eval 66.4%

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

   7. Simplified 66.4%

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

   8. Taylor expanded in t around 0 85.5%

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

   if -3.4999999999999998e99 < b < 7.19999999999999966e27

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unsub-neg 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in b around 0 77.3%

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

      1. *-commutative 77.3%

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

      2. div-exp 77.3%

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

      3. *-commutative 77.3%

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

      4. exp-to-pow 77.3%

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

      5. rem-exp-log 78.4%

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

   8. Simplified 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/l* 76.6%

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

   10. Applied egg-rr 76.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+99} \lor \neg \left(b \leq 7.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+192}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.5e+192)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e+192) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.5d+192)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e+192) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.5e+192:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.5e+192)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.5e+192)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.5e+192], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999965e192

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. div-exp 58.8%

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

      2. exp-to-pow 58.8%

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

      3. sub-neg 58.8%

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

      4. metadata-eval 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in t around 0 48.2%

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

   7. Taylor expanded in b around 0 19.5%

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

   8. Taylor expanded in x around 0 65.8%

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

   if -8.49999999999999965e192 < t

   1. Initial program 98.4%

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

      1. associate-/l* 97.4%

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

      2. associate--l+ 97.4%

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

      3. exp-sum 80.6%

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

      4. associate-/l* 78.1%

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

      5. *-commutative 78.1%

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

      6. exp-to-pow 78.1%

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

      7. exp-diff 71.0%

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

      8. *-commutative 71.0%

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

      9. exp-to-pow 71.6%

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

      10. sub-neg 71.6%

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

      11. metadata-eval 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in y around 0 66.2%

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

      1. associate-/r* 64.6%

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

      2. exp-to-pow 65.1%

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

      3. sub-neg 65.1%

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

      4. metadata-eval 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in t around 0 62.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+192}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.8e+67) (/ (/ x (* a (exp b))) y) (/ x (* b (* a (+ y (/ y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.8e+67) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.8d+67) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = x / (b * (a * (y + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.8e+67) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = x / (b * (a * (y + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.8e+67:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = x / (b * (a * (y + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.8e+67)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.8e+67)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = x / (b * (a * (y + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.8e+67], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7999999999999999e67

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 86.6%

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

      1. div-exp 73.5%

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

      2. exp-to-pow 74.3%

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

      3. sub-neg 74.3%

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

      4. metadata-eval 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around 0 69.0%

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

   if 1.7999999999999999e67 < y

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 68.0%

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

      4. associate-/l* 58.0%

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

      5. *-commutative 58.0%

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

      6. exp-to-pow 58.0%

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

      7. exp-diff 52.0%

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

      8. *-commutative 52.0%

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

      9. exp-to-pow 52.0%

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

      10. sub-neg 52.0%

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

      11. metadata-eval 52.0%

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

   3. Simplified 52.0%

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

   5. Taylor expanded in y around 0 38.9%

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

      1. associate-/r* 38.9%

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

      2. exp-to-pow 38.9%

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

      3. sub-neg 38.9%

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

      4. metadata-eval 38.9%

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

   7. Simplified 38.9%

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

   8. Taylor expanded in t around 0 36.3%

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

   9. Taylor expanded in b around 0 36.4%

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

   10. Taylor expanded in b around inf 33.4%

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

       1. associate-/l* 41.2%

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

       2. distribute-lft-out 43.2%

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

   12. Simplified 43.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-159}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.7e-159)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 5.2e-303)
     (/ x (* b (* a (+ y (/ y b)))))
     (if (<= b 1.4e+97)
       (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y)
       (/
        x
        (*
         a
         (+
          y
          (*
           b
           (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.7e-159) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 5.2e-303) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 1.4e+97) {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.7d-159)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 5.2d-303) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 1.4d+97) then
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    else
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.7e-159) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 5.2e-303) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 1.4e+97) {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.7e-159:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 5.2e-303:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 1.4e+97:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	else:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.7e-159)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 5.2e-303)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 1.4e+97)
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.7e-159)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 5.2e-303)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 1.4e+97)
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	else
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.7e-159], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.2e-303], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+97], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.7e-159

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 71.0%

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

   7. Taylor expanded in b around 0 44.6%

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

   8. Taylor expanded in x around 0 60.5%

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

   if -2.7e-159 < b < 5.20000000000000009e-303

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. associate-/r* 58.7%

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

      2. exp-to-pow 59.4%

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

      3. sub-neg 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 36.1%

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

   10. Taylor expanded in b around inf 34.6%

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

       1. associate-/l* 51.3%

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

       2. distribute-lft-out 51.4%

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

   12. Simplified 51.4%

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

   if 5.20000000000000009e-303 < b < 1.4e97

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 72.0%

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

      1. div-exp 68.3%

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

      2. exp-to-pow 69.7%

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

      3. sub-neg 69.7%

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

      4. metadata-eval 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in t around 0 56.7%

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

   7. Taylor expanded in b around 0 49.9%

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

   if 1.4e97 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 69.2%

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

      4. associate-/l* 69.2%

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

      5. *-commutative 69.2%

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

      6. exp-to-pow 69.2%

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

      7. exp-diff 56.4%

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

      8. *-commutative 56.4%

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

      9. exp-to-pow 56.4%

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

      10. sub-neg 56.4%

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

      11. metadata-eval 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in y around 0 69.3%

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

      1. associate-/r* 64.2%

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

      2. exp-to-pow 64.2%

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

      3. sub-neg 64.2%

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

      4. metadata-eval 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in t around 0 77.3%

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

   9. Taylor expanded in b around 0 72.4%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-159}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.6% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -2 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(b \cdot \left(t\_1 - \frac{x \cdot b}{y \cdot a}\right) - t\_1\right) + t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -2e-122)
     (+ (* b (- (* b (- t_1 (/ (* x b) (* y a)))) t_1)) t_1)
     (if (<= b 2.1e-301)
       (/ x (* b (* a (+ y (/ y b)))))
       (/
        (/
         x
         (+ a (* b (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
        y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -2e-122) {
		tmp = (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1)) + t_1;
	} else if (b <= 2.1e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-2d-122)) then
        tmp = (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1)) + t_1
    else if (b <= 2.1d-301) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -2e-122) {
		tmp = (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1)) + t_1;
	} else if (b <= 2.1e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -2e-122:
		tmp = (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1)) + t_1
	elif b <= 2.1e-301:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -2e-122)
		tmp = Float64(Float64(b * Float64(Float64(b * Float64(t_1 - Float64(Float64(x * b) / Float64(y * a)))) - t_1)) + t_1);
	elseif (b <= 2.1e-301)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -2e-122)
		tmp = (b * ((b * (t_1 - ((x * b) / (y * a)))) - t_1)) + t_1;
	elseif (b <= 2.1e-301)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e-122], N[(N[(b * N[(N[(b * N[(t$95$1 - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 2.1e-301], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.00000000000000012e-122

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

      3. exp-sum 77.5%

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

      4. associate-/l* 77.5%

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

      5. *-commutative 77.5%

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

      6. exp-to-pow 77.5%

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

      7. exp-diff 63.7%

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

      8. *-commutative 63.7%

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

      9. exp-to-pow 63.8%

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

      10. sub-neg 63.8%

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

      11. metadata-eval 63.8%

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

   3. Simplified 63.8%

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

   5. Taylor expanded in y around 0 67.1%

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

      1. associate-/r* 66.0%

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

      2. exp-to-pow 66.1%

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

      3. sub-neg 66.1%

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

      4. metadata-eval 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in t around 0 72.9%

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

   9. Taylor expanded in b around 0 20.2%

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

   10. Taylor expanded in b around 0 61.8%

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

   if -2.00000000000000012e-122 < b < 2.0999999999999999e-301

   1. Initial program 94.0%

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

      1. associate-/l* 94.1%

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

      2. associate--l+ 94.1%

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

      3. exp-sum 82.2%

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

      4. associate-/l* 77.4%

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

      5. *-commutative 77.4%

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

      6. exp-to-pow 77.4%

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

      7. exp-diff 77.4%

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

      8. *-commutative 77.4%

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

      9. exp-to-pow 78.7%

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

      10. sub-neg 78.7%

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

      11. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. associate-/r* 60.6%

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

      2. exp-to-pow 61.6%

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

      3. sub-neg 61.6%

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

      4. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in t around 0 37.6%

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

   9. Taylor expanded in b around 0 37.6%

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

   10. Taylor expanded in b around inf 36.4%

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

       1. associate-/l* 50.2%

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

       2. distribute-lft-out 50.3%

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

   12. Simplified 50.3%

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

   if 2.0999999999999999e-301 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

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

      1. div-exp 68.6%

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

      2. exp-to-pow 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 63.4%

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

   7. Taylor expanded in b around 0 54.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(b \cdot \left(\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\right) - \frac{x}{y \cdot a}\right) + \frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.3% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.85e-156)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 2.8e-301)
     (/ x (* b (* a (+ y (/ y b)))))
     (/
      (/
       x
       (+ a (* b (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.85e-156) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 2.8e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.85d-156)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 2.8d-301) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.85e-156) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 2.8e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.85e-156:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 2.8e-301:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.85e-156)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 2.8e-301)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.85e-156)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 2.8e-301)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.85e-156], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.8e-301], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.84999999999999993e-156

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 71.0%

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

   7. Taylor expanded in b around 0 44.6%

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

   8. Taylor expanded in x around 0 60.5%

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

   if -2.84999999999999993e-156 < b < 2.8000000000000001e-301

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. associate-/r* 58.7%

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

      2. exp-to-pow 59.4%

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

      3. sub-neg 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 36.1%

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

   10. Taylor expanded in b around inf 34.6%

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

       1. associate-/l* 51.3%

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

       2. distribute-lft-out 51.4%

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

   12. Simplified 51.4%

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

   if 2.8000000000000001e-301 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

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

      1. div-exp 68.6%

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

      2. exp-to-pow 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 63.4%

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

   7. Taylor expanded in b around 0 54.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{b \cdot \left(b \cdot \left(x - x \cdot 0.5\right) - x\right)}{a} + \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.95e-156)
   (/ (+ (/ (* b (- (* b (- x (* x 0.5))) x)) a) (/ x a)) y)
   (if (<= b 3.1e-302)
     (/ x (* b (* a (+ y (/ y b)))))
     (/
      (/
       x
       (+ a (* b (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e-156) {
		tmp = (((b * ((b * (x - (x * 0.5))) - x)) / a) + (x / a)) / y;
	} else if (b <= 3.1e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.95d-156)) then
        tmp = (((b * ((b * (x - (x * 0.5d0))) - x)) / a) + (x / a)) / y
    else if (b <= 3.1d-302) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e-156) {
		tmp = (((b * ((b * (x - (x * 0.5))) - x)) / a) + (x / a)) / y;
	} else if (b <= 3.1e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.95e-156:
		tmp = (((b * ((b * (x - (x * 0.5))) - x)) / a) + (x / a)) / y
	elif b <= 3.1e-302:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.95e-156)
		tmp = Float64(Float64(Float64(Float64(b * Float64(Float64(b * Float64(x - Float64(x * 0.5))) - x)) / a) + Float64(x / a)) / y);
	elseif (b <= 3.1e-302)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.95e-156)
		tmp = (((b * ((b * (x - (x * 0.5))) - x)) / a) + (x / a)) / y;
	elseif (b <= 3.1e-302)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.95e-156], N[(N[(N[(N[(b * N[(N[(b * N[(x - N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.1e-302], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9500000000000001e-156

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 71.0%

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

   7. Taylor expanded in b around 0 44.6%

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

   8. Taylor expanded in a around 0 60.5%

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

   if -1.9500000000000001e-156 < b < 3.09999999999999983e-302

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. associate-/r* 58.7%

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

      2. exp-to-pow 59.4%

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

      3. sub-neg 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 36.1%

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

   10. Taylor expanded in b around inf 34.6%

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

       1. associate-/l* 51.3%

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

       2. distribute-lft-out 51.4%

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

   12. Simplified 51.4%

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

   if 3.09999999999999983e-302 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

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

      1. div-exp 68.6%

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

      2. exp-to-pow 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 63.4%

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

   7. Taylor expanded in b around 0 54.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{b \cdot \left(b \cdot \left(x - x \cdot 0.5\right) - x\right)}{a} + \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.5% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e-157)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 2.3e-301)
     (/ x (* b (* a (+ y (/ y b)))))
     (if (<= b 1.18e+110)
       (/ (/ x (+ a (* a b))) y)
       (/ x (* a (* y (- 1.0 (* b (- -1.0 (* b 0.5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e-157) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2.3e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 1.18e+110) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.8d-157)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 2.3d-301) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 1.18d+110) then
        tmp = (x / (a + (a * b))) / y
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e-157) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2.3e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 1.18e+110) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e-157:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 2.3e-301:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 1.18e+110:
		tmp = (x / (a + (a * b))) / y
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e-157)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 2.3e-301)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 1.18e+110)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e-157)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 2.3e-301)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 1.18e+110)
		tmp = (x / (a + (a * b))) / y;
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e-157], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.3e-301], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.18e+110], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.79999999999999955e-157

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 71.0%

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

   7. Taylor expanded in b around 0 51.1%

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

   if -6.79999999999999955e-157 < b < 2.3000000000000002e-301

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. associate-/r* 58.7%

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

      2. exp-to-pow 59.4%

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

      3. sub-neg 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 36.1%

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

   10. Taylor expanded in b around inf 34.6%

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

       1. associate-/l* 51.3%

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

       2. distribute-lft-out 51.4%

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

   12. Simplified 51.4%

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

   if 2.3000000000000002e-301 < b < 1.1799999999999999e110

   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. Add Preprocessing

   3. Taylor expanded in y around 0 73.0%

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

      1. div-exp 68.2%

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

      2. exp-to-pow 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 57.1%

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

   7. Taylor expanded in b around 0 49.4%

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

   if 1.1799999999999999e110 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 69.4%

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

      4. associate-/l* 69.4%

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

      5. *-commutative 69.4%

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

      6. exp-to-pow 69.4%

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

      7. exp-diff 55.6%

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

      8. *-commutative 55.6%

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

      9. exp-to-pow 55.6%

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

      10. sub-neg 55.6%

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

      11. metadata-eval 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. associate-/r* 64.0%

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

      2. exp-to-pow 64.0%

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

      3. sub-neg 64.0%

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

      4. metadata-eval 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in t around 0 78.1%

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

   9. Taylor expanded in b around 0 68.0%

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

       1. associate-*r* 68.0%

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

   11. Simplified 68.0%

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

   12. Taylor expanded in y around 0 70.5%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.3% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.7e-157)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 2.1e-301)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.7e-157) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2.1e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.7d-157)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 2.1d-301) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.7e-157) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2.1e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.7e-157:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 2.1e-301:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.7e-157)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 2.1e-301)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.7e-157)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 2.1e-301)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.7e-157], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.1e-301], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.7000000000000002e-157

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 71.0%

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

   7. Taylor expanded in b around 0 51.1%

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

   if -4.7000000000000002e-157 < b < 2.0999999999999999e-301

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. associate-/r* 58.7%

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

      2. exp-to-pow 59.4%

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

      3. sub-neg 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 36.1%

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

   10. Taylor expanded in b around inf 34.6%

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

       1. associate-/l* 51.3%

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

       2. distribute-lft-out 51.4%

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

   12. Simplified 51.4%

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

   if 2.0999999999999999e-301 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

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

      1. div-exp 68.6%

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

      2. exp-to-pow 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 63.4%

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

   7. Taylor expanded in b around 0 53.5%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.8% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.6e-150)
   (/ (- x (* b (+ x (* b (* x -0.5))))) (* y a))
   (if (<= b 9.5e-302)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.6e-150) {
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	} else if (b <= 9.5e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.6d-150)) then
        tmp = (x - (b * (x + (b * (x * (-0.5d0)))))) / (y * a)
    else if (b <= 9.5d-302) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.6e-150) {
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	} else if (b <= 9.5e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.6e-150:
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a)
	elif b <= 9.5e-302:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.6e-150)
		tmp = Float64(Float64(x - Float64(b * Float64(x + Float64(b * Float64(x * -0.5))))) / Float64(y * a));
	elseif (b <= 9.5e-302)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.6e-150)
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	elseif (b <= 9.5e-302)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.6e-150], N[(N[(x - N[(b * N[(x + N[(b * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-302], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.6e-150

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 85.7%

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

      1. div-exp 66.5%

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

      2. exp-to-pow 67.0%

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

      3. sub-neg 67.0%

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

      4. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around 0 71.4%

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

   7. Taylor expanded in b around 0 44.5%

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

   8. Taylor expanded in a around 0 58.9%

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

      1. *-commutative 58.9%

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

      2. associate-*r* 58.9%

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

      3. mul-1-neg 58.9%

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

      4. distribute-rgt-out 58.9%

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

      5. metadata-eval 58.9%

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

   10. Simplified 58.9%

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

   if -9.6e-150 < b < 9.49999999999999991e-302

   1. Initial program 94.2%

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

      1. associate-/l* 96.4%

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

      2. associate--l+ 96.4%

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

      3. exp-sum 85.6%

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

      4. associate-/l* 80.2%

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

      5. *-commutative 80.2%

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

      6. exp-to-pow 80.2%

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

      7. exp-diff 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 81.1%

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

      10. sub-neg 81.1%

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

      11. metadata-eval 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in y around 0 58.4%

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

      1. associate-/r* 58.4%

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

      2. exp-to-pow 59.0%

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

      3. sub-neg 59.0%

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

      4. metadata-eval 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in t around 0 34.3%

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

   9. Taylor expanded in b around 0 34.3%

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

   10. Taylor expanded in b around inf 32.9%

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

       1. associate-/l* 48.7%

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

       2. distribute-lft-out 48.7%

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

   12. Simplified 48.7%

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

   if 9.49999999999999991e-302 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

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

      1. div-exp 68.6%

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

      2. exp-to-pow 69.6%

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

      3. sub-neg 69.6%

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

      4. metadata-eval 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0 63.4%

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

   7. Taylor expanded in b around 0 53.5%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.1% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e-158)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 2.8e-301)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e-158) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 2.8e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.8d-158)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 2.8d-301) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e-158) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 2.8e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.8e-158:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 2.8e-301:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e-158)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 2.8e-301)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.8e-158)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 2.8e-301)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e-158], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.8e-301], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.80000000000000002e-158

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 71.0%

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

   7. Taylor expanded in b around 0 44.6%

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

   8. Taylor expanded in x around 0 60.5%

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

   if -2.80000000000000002e-158 < b < 2.8000000000000001e-301

   1. Initial program 94.1%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. associate-/r* 58.7%

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

      2. exp-to-pow 59.4%

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

      3. sub-neg 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 36.1%

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

   10. Taylor expanded in b around inf 34.6%

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

       1. associate-/l* 51.3%

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

       2. distribute-lft-out 51.4%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   12. Simplified 51.4%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 2.8000000000000001e-301 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 63.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 53.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.7% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e-150)
   (* (/ x (* y a)) (- (- -1.0) b))
   (if (<= b 1.15e-302)
     (/ x (* b (* a (+ y (/ y 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 <= -1.2e-150) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else if (b <= 1.15e-302) {
		tmp = x / (b * (a * (y + (y / 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 <= (-1.2d-150)) then
        tmp = (x / (y * a)) * (-(-1.0d0) - b)
    else if (b <= 1.15d-302) then
        tmp = x / (b * (a * (y + (y / 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 <= -1.2e-150) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else if (b <= 1.15e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e-150:
		tmp = (x / (y * a)) * (-(-1.0) - b)
	elif b <= 1.15e-302:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e-150)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(Float64(-(-1.0)) - b));
	elseif (b <= 1.15e-302)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / 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 <= -1.2e-150)
		tmp = (x / (y * a)) * (-(-1.0) - b);
	elseif (b <= 1.15e-302)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e-150], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-302], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $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 < -1.2e-150

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 76.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 76.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 76.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 76.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 63.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 63.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 63.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 63.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 63.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.6%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 66.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 66.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 66.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 66.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 66.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 72.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 22.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around 0 50.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 50.1%

          \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

       2. remove-double-neg 50.1%

          \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. distribute-neg-out 50.1%

          \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       4. associate-/l* 43.4%

          \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} + \left(-\frac{x}{a \cdot y}\right)\right) \]

       5. mul-1-neg 43.4%

          \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} + \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       6. distribute-rgt-out 43.4%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

       7. *-commutative 43.4%

          \[\leadsto -\frac{x}{\color{blue}{y \cdot a}} \cdot \left(b + -1\right) \]

   12. Simplified 43.4%

       \[\leadsto \color{blue}{-\frac{x}{y \cdot a} \cdot \left(b + -1\right)} \]

   if -1.2e-150 < b < 1.15000000000000001e-302

   1. Initial program 94.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 58.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 58.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 59.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 59.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 59.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 59.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 34.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around inf 32.9%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   11. Step-by-step derivation

       1. associate-/l* 48.7%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 48.7%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   12. Simplified 48.7%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 1.15000000000000001e-302 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 63.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 47.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 40.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.72e-156)
   (/ (- (/ x a) (* b (/ x a))) y)
   (if (<= b 6.2e-302)
     (/ x (* b (* a (+ y (/ y 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 <= -1.72e-156) {
		tmp = ((x / a) - (b * (x / a))) / y;
	} else if (b <= 6.2e-302) {
		tmp = x / (b * (a * (y + (y / 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 <= (-1.72d-156)) then
        tmp = ((x / a) - (b * (x / a))) / y
    else if (b <= 6.2d-302) then
        tmp = x / (b * (a * (y + (y / 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 <= -1.72e-156) {
		tmp = ((x / a) - (b * (x / a))) / y;
	} else if (b <= 6.2e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.72e-156:
		tmp = ((x / a) - (b * (x / a))) / y
	elif b <= 6.2e-302:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.72e-156)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(x / a))) / y);
	elseif (b <= 6.2e-302)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / 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 <= -1.72e-156)
		tmp = ((x / a) - (b * (x / a))) / y;
	elseif (b <= 6.2e-302)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.72e-156], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.2e-302], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $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 < -1.7199999999999999e-156

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 67.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 67.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 67.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 67.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 51.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 51.1%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 51.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 46.3%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 46.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   if -1.7199999999999999e-156 < b < 6.19999999999999967e-302

   1. Initial program 94.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 87.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 58.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 58.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 59.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 59.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 59.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 59.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 36.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 36.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around inf 34.6%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   11. Step-by-step derivation

       1. associate-/l* 51.3%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 51.4%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   12. Simplified 51.4%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 6.19999999999999967e-302 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 63.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 47.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 41.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1)
   (- (/ x (* y a)) (* (/ x a) (/ b y)))
   (if (<= b 1.5e-301)
     (/ x (* b (* a (+ y (/ y 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 <= -1.1) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 1.5e-301) {
		tmp = x / (b * (a * (y + (y / 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 <= (-1.1d0)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= 1.5d-301) then
        tmp = x / (b * (a * (y + (y / 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 <= -1.1) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 1.5e-301) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= 1.5e-301:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= 1.5e-301)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / 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 <= -1.1)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= 1.5e-301)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-301], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $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 < -1.1000000000000001

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 73.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 73.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 73.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 73.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 54.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 54.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 54.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 54.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 54.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 54.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.3%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 61.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 61.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 61.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 61.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 61.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 82.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 50.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. +-commutative 50.3%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

       2. mul-1-neg 50.3%

          \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

       3. unsub-neg 50.3%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

       4. *-commutative 50.3%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} - \frac{b \cdot x}{a \cdot y} \]

       5. *-commutative 50.3%

          \[\leadsto \frac{x}{y \cdot a} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

       6. times-frac 47.5%

          \[\leadsto \frac{x}{y \cdot a} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   11. Simplified 47.5%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}} \]

   if -1.1000000000000001 < b < 1.5e-301

   1. Initial program 96.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.8%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 66.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 67.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 67.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 67.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 67.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 41.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 41.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around inf 34.7%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   11. Step-by-step derivation

       1. associate-/l* 44.7%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 49.2%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   12. Simplified 49.2%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 1.5e-301 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 63.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 47.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 41.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.4e-156)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 3.3e-302)
     (/ x (* b (* a (+ y (/ y 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 <= -2.4e-156) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 3.3e-302) {
		tmp = x / (b * (a * (y + (y / 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 <= (-2.4d-156)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 3.3d-302) then
        tmp = x / (b * (a * (y + (y / 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 <= -2.4e-156) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 3.3e-302) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.4e-156:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 3.3e-302:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.4e-156)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 3.3e-302)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / 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 <= -2.4e-156)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 3.3e-302)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.4e-156], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.3e-302], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $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 < -2.4e-156

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 67.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 67.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 67.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 67.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 67.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 51.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   if -2.4e-156 < b < 3.3000000000000002e-302

   1. Initial program 94.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 87.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 58.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 58.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 59.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 59.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 59.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 59.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 36.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 36.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around inf 34.6%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   11. Step-by-step derivation

       1. associate-/l* 51.3%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 51.4%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   12. Simplified 51.4%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 3.3000000000000002e-302 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 63.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 47.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.6% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.55 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.55e-296)
   (* (/ x (* y a)) (- (- -1.0) 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 <= 1.55e-296) {
		tmp = (x / (y * a)) * (-(-1.0) - 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 <= 1.55d-296) then
        tmp = (x / (y * a)) * (-(-1.0d0) - 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 <= 1.55e-296) {
		tmp = (x / (y * a)) * (-(-1.0) - b);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.55e-296:
		tmp = (x / (y * a)) * (-(-1.0) - b)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.55e-296)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(Float64(-(-1.0)) - 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 <= 1.55e-296)
		tmp = (x / (y * a)) * (-(-1.0) - b);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.55e-296], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[((--1.0) - b), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.5500000000000001e-296

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 79.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 77.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 77.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 77.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 68.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 68.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 68.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 68.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 68.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 64.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 64.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 64.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 64.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 64.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 61.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 25.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around 0 45.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 45.1%

          \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

       2. remove-double-neg 45.1%

          \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. distribute-neg-out 45.1%

          \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       4. associate-/l* 40.4%

          \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} + \left(-\frac{x}{a \cdot y}\right)\right) \]

       5. mul-1-neg 40.4%

          \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} + \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       6. distribute-rgt-out 40.4%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

       7. *-commutative 40.4%

          \[\leadsto -\frac{x}{\color{blue}{y \cdot a}} \cdot \left(b + -1\right) \]

   12. Simplified 40.4%

       \[\leadsto \color{blue}{-\frac{x}{y \cdot a} \cdot \left(b + -1\right)} \]

   if 1.5500000000000001e-296 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 64.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.4%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.55 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(\left(--1\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 35.5% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.8 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.8e-292) (* (/ x y) (/ 1.0 a)) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.8e-292) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.8d-292) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.8e-292) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.8e-292:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.8e-292)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.8e-292)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.8e-292], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.8000000000000002e-292

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 81.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 81.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 81.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 81.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 57.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   7. Step-by-step derivation

      1. div-exp 57.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 57.3%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 57.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 57.8%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      5. associate-/l* 57.8%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      6. associate-/r* 56.2%

         \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]

      7. *-commutative 56.2%

         \[\leadsto \frac{\color{blue}{{z}^{y} \cdot x}}{a \cdot y} \]

      8. times-frac 56.2%

         \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y}} \]

   8. Simplified 56.2%

      \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y}} \]

   9. Taylor expanded in y around 0 35.4%

      \[\leadsto \color{blue}{\frac{1}{a}} \cdot \frac{x}{y} \]

   if 3.8000000000000002e-292 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 79.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 68.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 69.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 64.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.4%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.8 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 34.7% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 11500:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 11500.0) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 11500.0) {
		tmp = (x / a) / 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 <= 11500.0d0) then
        tmp = (x / a) / 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 <= 11500.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 11500.0:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 11500.0)
		tmp = Float64(Float64(x / a) / 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 <= 11500.0)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 11500.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 11500

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 83.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 83.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 83.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 83.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 66.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]

      2. div-exp 66.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}} \cdot x}{y} \]

      3. *-commutative 66.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}} \cdot x}{y} \]

      4. exp-to-pow 66.5%

         \[\leadsto \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}} \cdot x}{y} \]

      5. rem-exp-log 67.4%

         \[\leadsto \frac{\frac{{z}^{y}}{\color{blue}{a}} \cdot x}{y} \]

   8. Simplified 67.4%

      \[\leadsto \frac{\color{blue}{\frac{{z}^{y}}{a} \cdot x}}{y} \]

   9. Taylor expanded in y around 0 38.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. associate-/r* 40.1%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   11. Simplified 40.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   if 11500 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 74.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 74.1%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 74.1%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 74.1%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 59.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 59.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 59.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 59.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 59.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 59.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.6%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.1%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.1%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.1%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 63.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 74.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]

   10. Taylor expanded in b around inf 42.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   11. Step-by-step derivation

       1. *-commutative 42.7%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   12. Simplified 42.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 11500:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 31.7% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+100}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4e+100) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4e+100) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 4d+100) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4e+100) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4e+100:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4e+100)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4e+100)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4e+100], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.00000000000000006e100

   1. Initial program 99.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 83.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 83.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 83.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 83.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 64.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 64.9%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]

      2. div-exp 64.9%

         \[\leadsto \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}} \cdot x}{y} \]

      3. *-commutative 64.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}} \cdot x}{y} \]

      4. exp-to-pow 64.9%

         \[\leadsto \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}} \cdot x}{y} \]

      5. rem-exp-log 65.6%

         \[\leadsto \frac{\frac{{z}^{y}}{\color{blue}{a}} \cdot x}{y} \]

   8. Simplified 65.6%

      \[\leadsto \frac{\color{blue}{\frac{{z}^{y}}{a} \cdot x}}{y} \]

   9. Taylor expanded in y around 0 30.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. associate-/r* 34.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   11. Simplified 34.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   if 4.00000000000000006e100 < a

   1. Initial program 96.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 86.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 86.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 86.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 86.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 86.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 57.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]

      2. div-exp 57.0%

         \[\leadsto \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}} \cdot x}{y} \]

      3. *-commutative 57.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}} \cdot x}{y} \]

      4. exp-to-pow 57.0%

         \[\leadsto \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}} \cdot x}{y} \]

      5. rem-exp-log 57.8%

         \[\leadsto \frac{\frac{{z}^{y}}{\color{blue}{a}} \cdot x}{y} \]

   8. Simplified 57.8%

      \[\leadsto \frac{\color{blue}{\frac{{z}^{y}}{a} \cdot x}}{y} \]

   9. Taylor expanded in y around 0 44.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 44.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 44.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+100}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 30.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 84.4%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
4. Step-by-step derivation

   1. +-commutative 84.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

   2. mul-1-neg 84.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   3. unsub-neg 84.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

5. Simplified 84.4%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

6. Taylor expanded in b around 0 62.5%

   \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]
7. Step-by-step derivation

   1. *-commutative 62.5%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]

   2. div-exp 62.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}} \cdot x}{y} \]

   3. *-commutative 62.5%

      \[\leadsto \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}} \cdot x}{y} \]

   4. exp-to-pow 62.5%

      \[\leadsto \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}} \cdot x}{y} \]

   5. rem-exp-log 63.2%

      \[\leadsto \frac{\frac{{z}^{y}}{\color{blue}{a}} \cdot x}{y} \]

8. Simplified 63.2%

   \[\leadsto \frac{\color{blue}{\frac{{z}^{y}}{a} \cdot x}}{y} \]

9. Taylor expanded in y around 0 34.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 34.9%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

11. Simplified 34.9%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

12. Final simplification 34.9%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Developer target: 72.4% 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 2024067 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))