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

Percentage Accurate: 98.3% → 98.3%

Time: 21.7s

Alternatives: 20

Speedup: 1.0×

• 47.0% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.9%

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

2. Final simplification 98.9%

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

Alternative 2: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0024 \lor \neg \left(y \leq 1.35 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0024) (not (<= y 1.35e-28)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0024) || !(y <= 1.35e-28)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-0.0024d0)) .or. (.not. (y <= 1.35d-28))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0024) || !(y <= 1.35e-28)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0024) or not (y <= 1.35e-28):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0024) || !(y <= 1.35e-28))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.0024) || ~((y <= 1.35e-28)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0024], N[Not[LessEqual[y, 1.35e-28]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00239999999999999979 or 1.3499999999999999e-28 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.6%

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

      1. +-commutative 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

   4. Simplified 92.6%

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

   if -0.00239999999999999979 < y < 1.3499999999999999e-28

   1. Initial program 97.9%

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

      1. associate-/l* 97.5%

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

      2. fma-def 97.5%

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

      3. sub-neg 97.5%

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

      4. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 97.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0024 \lor \neg \left(y \leq 1.35 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]

Alternative 3: 88.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ t_2 := \frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y))
        (t_2 (/ x (* y (/ a (pow z y))))))
   (if (<= y -2.65e+91)
     t_2
     (if (<= y -4.5e+44)
       t_1
       (if (<= y -4.6e-40)
         (* (/ x (* y (exp b))) (/ (pow z y) a))
         (if (<= y 9.5e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	double t_2 = x / (y * (a / pow(z, y)));
	double tmp;
	if (y <= -2.65e+91) {
		tmp = t_2;
	} else if (y <= -4.5e+44) {
		tmp = t_1;
	} else if (y <= -4.6e-40) {
		tmp = (x / (y * exp(b))) * (pow(z, y) / a);
	} else if (y <= 9.5e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    t_2 = x / (y * (a / (z ** y)))
    if (y <= (-2.65d+91)) then
        tmp = t_2
    else if (y <= (-4.5d+44)) then
        tmp = t_1
    else if (y <= (-4.6d-40)) then
        tmp = (x / (y * exp(b))) * ((z ** y) / a)
    else if (y <= 9.5d+84) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	double t_2 = x / (y * (a / Math.pow(z, y)));
	double tmp;
	if (y <= -2.65e+91) {
		tmp = t_2;
	} else if (y <= -4.5e+44) {
		tmp = t_1;
	} else if (y <= -4.6e-40) {
		tmp = (x / (y * Math.exp(b))) * (Math.pow(z, y) / a);
	} else if (y <= 9.5e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	t_2 = x / (y * (a / math.pow(z, y)))
	tmp = 0
	if y <= -2.65e+91:
		tmp = t_2
	elif y <= -4.5e+44:
		tmp = t_1
	elif y <= -4.6e-40:
		tmp = (x / (y * math.exp(b))) * (math.pow(z, y) / a)
	elif y <= 9.5e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y)
	t_2 = Float64(x / Float64(y * Float64(a / (z ^ y))))
	tmp = 0.0
	if (y <= -2.65e+91)
		tmp = t_2;
	elseif (y <= -4.5e+44)
		tmp = t_1;
	elseif (y <= -4.6e-40)
		tmp = Float64(Float64(x / Float64(y * exp(b))) * Float64((z ^ y) / a));
	elseif (y <= 9.5e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	t_2 = x / (y * (a / (z ^ y)));
	tmp = 0.0;
	if (y <= -2.65e+91)
		tmp = t_2;
	elseif (y <= -4.5e+44)
		tmp = t_1;
	elseif (y <= -4.6e-40)
		tmp = (x / (y * exp(b))) * ((z ^ y) / a);
	elseif (y <= 9.5e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+91], t$95$2, If[LessEqual[y, -4.5e+44], t$95$1, If[LessEqual[y, -4.6e-40], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.64999999999999998e91 or 9.49999999999999979e84 < 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/ 87.6%

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

      2. associate--l+ 87.6%

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

      3. exp-sum 57.7%

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

      4. associate-*r* 57.7%

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

      5. *-commutative 57.7%

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

      6. exp-to-pow 57.7%

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

      7. exp-diff 56.7%

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

      8. *-commutative 56.7%

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

      9. exp-to-pow 56.7%

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

      10. sub-neg 56.7%

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

      11. metadata-eval 56.7%

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

   3. Simplified 56.7%

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

   4. Taylor expanded in t around 0 66.0%

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

      1. *-commutative 66.0%

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

      2. times-frac 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in b around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. clear-num 80.5%

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

      3. frac-times 90.9%

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

      4. *-un-lft-identity 90.9%

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

   9. Applied egg-rr 90.9%

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

   if -2.64999999999999998e91 < y < -4.5e44 or -4.6e-40 < y < 9.49999999999999979e84

   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* 98.0%

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

      2. fma-def 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around 0 95.6%

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

   if -4.5e44 < y < -4.6e-40

   1. Initial program 97.8%

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

      1. associate-*l/ 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 92.1%

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

      4. associate-*r* 92.1%

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

      5. *-commutative 92.1%

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

      6. exp-to-pow 92.1%

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

      7. exp-diff 92.1%

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

      8. *-commutative 92.1%

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

      9. exp-to-pow 94.1%

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

      10. sub-neg 94.1%

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

      11. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 93.9%

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

      1. *-commutative 93.9%

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

      2. times-frac 94.1%

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

   6. Simplified 94.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \end{array} \]

Alternative 4: 77.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -9000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-222}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -9000000.0)
     t_1
     (if (<= t 6.6e-268)
       (/ x (* y (/ a (pow z y))))
       (if (<= t 1.08e-222)
         (/ (/ x (* a (exp b))) y)
         (if (<= t 1.02e-7) (* (/ x (* y (exp b))) (/ (pow z y) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -9000000.0) {
		tmp = t_1;
	} else if (t <= 6.6e-268) {
		tmp = x / (y * (a / pow(z, y)));
	} else if (t <= 1.08e-222) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 1.02e-7) {
		tmp = (x / (y * exp(b))) * (pow(z, y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-9000000.0d0)) then
        tmp = t_1
    else if (t <= 6.6d-268) then
        tmp = x / (y * (a / (z ** y)))
    else if (t <= 1.08d-222) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 1.02d-7) then
        tmp = (x / (y * exp(b))) * ((z ** y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -9000000.0) {
		tmp = t_1;
	} else if (t <= 6.6e-268) {
		tmp = x / (y * (a / Math.pow(z, y)));
	} else if (t <= 1.08e-222) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 1.02e-7) {
		tmp = (x / (y * Math.exp(b))) * (Math.pow(z, y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -9000000.0:
		tmp = t_1
	elif t <= 6.6e-268:
		tmp = x / (y * (a / math.pow(z, y)))
	elif t <= 1.08e-222:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 1.02e-7:
		tmp = (x / (y * math.exp(b))) * (math.pow(z, y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -9000000.0)
		tmp = t_1;
	elseif (t <= 6.6e-268)
		tmp = Float64(x / Float64(y * Float64(a / (z ^ y))));
	elseif (t <= 1.08e-222)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 1.02e-7)
		tmp = Float64(Float64(x / Float64(y * exp(b))) * Float64((z ^ y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -9000000.0)
		tmp = t_1;
	elseif (t <= 6.6e-268)
		tmp = x / (y * (a / (z ^ y)));
	elseif (t <= 1.08e-222)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 1.02e-7)
		tmp = (x / (y * exp(b))) * ((z ^ y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -9000000.0], t$95$1, If[LessEqual[t, 6.6e-268], N[(x / N[(y * N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e-222], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.02e-7], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9e6 or 1.02e-7 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.9%

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

      1. exp-diff 73.3%

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

      2. exp-to-pow 73.3%

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

      3. sub-neg 73.3%

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

      4. metadata-eval 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in b around 0 85.3%

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

      1. exp-to-pow 85.3%

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

      2. sub-neg 85.3%

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

      3. metadata-eval 85.3%

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

      4. +-commutative 85.3%

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

   7. Simplified 85.3%

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

   if -9e6 < t < 6.59999999999999986e-268

   1. Initial program 97.2%

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

      1. associate-*l/ 93.3%

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

      2. associate--l+ 93.3%

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

      3. exp-sum 76.0%

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

      4. associate-*r* 76.0%

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

      5. *-commutative 76.0%

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

      6. exp-to-pow 76.0%

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

      7. exp-diff 76.0%

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

      8. *-commutative 76.0%

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

      9. exp-to-pow 76.9%

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

      10. sub-neg 76.9%

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

      11. metadata-eval 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. times-frac 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in b around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. clear-num 78.8%

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

      3. frac-times 83.1%

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

      4. *-un-lft-identity 83.1%

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

   9. Applied egg-rr 83.1%

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

   if 6.59999999999999986e-268 < t < 1.07999999999999995e-222

   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. Taylor expanded in y around 0 89.8%

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

      1. exp-diff 89.8%

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

      2. exp-to-pow 91.3%

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

      3. sub-neg 91.3%

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

      4. metadata-eval 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in t around 0 91.3%

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

   if 1.07999999999999995e-222 < t < 1.02e-7

   1. Initial program 98.9%

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

      1. associate-*l/ 82.5%

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

      2. associate--l+ 82.5%

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

      3. exp-sum 78.4%

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

      4. associate-*r* 78.4%

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

      5. *-commutative 78.4%

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

      6. exp-to-pow 78.4%

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

      7. exp-diff 78.4%

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

      8. *-commutative 78.4%

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

      9. exp-to-pow 79.5%

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

      10. sub-neg 79.5%

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

      11. metadata-eval 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around 0 87.8%

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

      1. *-commutative 87.8%

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

      2. times-frac 89.7%

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

   6. Simplified 89.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-222}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 5: 82.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0024 \lor \neg \left(y \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0024) (not (<= y 1.9e+80)))
   (/ x (* y (/ a (pow z y))))
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0024) || !(y <= 1.9e+80)) {
		tmp = x / (y * (a / pow(z, y)));
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-0.0024d0)) .or. (.not. (y <= 1.9d+80))) then
        tmp = x / (y * (a / (z ** y)))
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0024) || !(y <= 1.9e+80)) {
		tmp = x / (y * (a / Math.pow(z, y)));
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0024) or not (y <= 1.9e+80):
		tmp = x / (y * (a / math.pow(z, y)))
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0024) || !(y <= 1.9e+80))
		tmp = Float64(x / Float64(y * Float64(a / (z ^ y))));
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.0024) || ~((y <= 1.9e+80)))
		tmp = x / (y * (a / (z ^ y)));
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0024], N[Not[LessEqual[y, 1.9e+80]], $MachinePrecision]], N[(x / N[(y * N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00239999999999999979 or 1.89999999999999999e80 < y

   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/ 89.8%

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

      2. associate--l+ 89.8%

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

      3. exp-sum 59.5%

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

      4. associate-*r* 59.5%

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

      5. *-commutative 59.5%

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

      6. exp-to-pow 59.5%

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

      7. exp-diff 57.9%

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

      8. *-commutative 57.9%

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

      9. exp-to-pow 58.0%

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

      10. sub-neg 58.0%

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

      11. metadata-eval 58.0%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in t around 0 65.6%

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

      1. *-commutative 65.6%

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

      2. times-frac 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in b around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. clear-num 78.3%

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

      3. frac-times 86.8%

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

      4. *-un-lft-identity 86.8%

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

   9. Applied egg-rr 86.8%

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

   if -0.00239999999999999979 < y < 1.89999999999999999e80

   1. Initial program 98.2%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. exp-diff 87.3%

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

      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%

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

   4. Simplified 88.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0024 \lor \neg \left(y \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 6: 75.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ t_2 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;y \leq -0.0024:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (/ a (pow z y))))) (t_2 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= y -0.0024)
     t_1
     (if (<= y -1.25e-110)
       (/ (/ x (* a (exp b))) y)
       (if (<= y 3.8e-172)
         t_2
         (if (<= y 4.5e-85)
           (/ x (* a (* y (exp b))))
           (if (<= y 4.5e-30) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * (a / pow(z, y)));
	double t_2 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (y <= -0.0024) {
		tmp = t_1;
	} else if (y <= -1.25e-110) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 3.8e-172) {
		tmp = t_2;
	} else if (y <= 4.5e-85) {
		tmp = x / (a * (y * exp(b)));
	} else if (y <= 4.5e-30) {
		tmp = t_2;
	} 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 / (y * (a / (z ** y)))
    t_2 = (x * (a ** (t + (-1.0d0)))) / y
    if (y <= (-0.0024d0)) then
        tmp = t_1
    else if (y <= (-1.25d-110)) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 3.8d-172) then
        tmp = t_2
    else if (y <= 4.5d-85) then
        tmp = x / (a * (y * exp(b)))
    else if (y <= 4.5d-30) then
        tmp = t_2
    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 / (y * (a / Math.pow(z, y)));
	double t_2 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (y <= -0.0024) {
		tmp = t_1;
	} else if (y <= -1.25e-110) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 3.8e-172) {
		tmp = t_2;
	} else if (y <= 4.5e-85) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (y <= 4.5e-30) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * (a / math.pow(z, y)))
	t_2 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if y <= -0.0024:
		tmp = t_1
	elif y <= -1.25e-110:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 3.8e-172:
		tmp = t_2
	elif y <= 4.5e-85:
		tmp = x / (a * (y * math.exp(b)))
	elif y <= 4.5e-30:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * Float64(a / (z ^ y))))
	t_2 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (y <= -0.0024)
		tmp = t_1;
	elseif (y <= -1.25e-110)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 3.8e-172)
		tmp = t_2;
	elseif (y <= 4.5e-85)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (y <= 4.5e-30)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * (a / (z ^ y)));
	t_2 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (y <= -0.0024)
		tmp = t_1;
	elseif (y <= -1.25e-110)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 3.8e-172)
		tmp = t_2;
	elseif (y <= 4.5e-85)
		tmp = x / (a * (y * exp(b)));
	elseif (y <= 4.5e-30)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -0.0024], t$95$1, If[LessEqual[y, -1.25e-110], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.8e-172], t$95$2, If[LessEqual[y, 4.5e-85], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-30], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.00239999999999999979 or 4.49999999999999967e-30 < y

   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/ 91.0%

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

      2. associate--l+ 91.0%

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

      3. exp-sum 61.1%

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

      4. associate-*r* 61.1%

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

      5. *-commutative 61.1%

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

      6. exp-to-pow 61.1%

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

      7. exp-diff 59.7%

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

      8. *-commutative 59.7%

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

      9. exp-to-pow 59.9%

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

      10. sub-neg 59.9%

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

      11. metadata-eval 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in t around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. times-frac 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in b around 0 77.6%

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

      1. *-commutative 77.6%

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

      2. clear-num 77.6%

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

      3. frac-times 84.9%

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

      4. *-un-lft-identity 84.9%

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

   9. Applied egg-rr 84.9%

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

   if -0.00239999999999999979 < y < -1.25e-110

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. exp-diff 90.9%

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

      2. exp-to-pow 91.9%

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

      3. sub-neg 91.9%

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

      4. metadata-eval 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in t around 0 84.5%

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

   if -1.25e-110 < y < 3.79999999999999987e-172 or 4.50000000000000004e-85 < y < 4.49999999999999967e-30

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 97.4%

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

      1. exp-diff 88.7%

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

      2. exp-to-pow 89.5%

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

      3. sub-neg 89.5%

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

      4. metadata-eval 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in b around 0 85.3%

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

      1. exp-to-pow 86.1%

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

      2. sub-neg 86.1%

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

      3. metadata-eval 86.1%

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

      4. +-commutative 86.1%

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

   7. Simplified 86.1%

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

   if 3.79999999999999987e-172 < y < 4.50000000000000004e-85

   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. Step-by-step derivation

      1. associate-*l/ 99.3%

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

      2. associate--l+ 99.3%

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

      3. exp-sum 99.3%

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

      4. associate-*r* 99.3%

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

      5. *-commutative 99.3%

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

      6. exp-to-pow 99.3%

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

      7. exp-diff 77.9%

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

      8. *-commutative 77.9%

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

      9. exp-to-pow 78.6%

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

      10. sub-neg 78.6%

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

      11. metadata-eval 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in t around 0 86.2%

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

      1. *-commutative 86.2%

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

      2. times-frac 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in y around 0 86.2%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0024:\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \end{array} \]

Alternative 7: 74.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0016 \lor \neg \left(y \leq 7 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0016) (not (<= y 7e+61)))
   (/ x (* y (/ a (pow z y))))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0016) || !(y <= 7e+61)) {
		tmp = x / (y * (a / pow(z, 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 ((y <= (-0.0016d0)) .or. (.not. (y <= 7d+61))) then
        tmp = x / (y * (a / (z ** 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 ((y <= -0.0016) || !(y <= 7e+61)) {
		tmp = x / (y * (a / Math.pow(z, y)));
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0016) or not (y <= 7e+61):
		tmp = x / (y * (a / math.pow(z, y)))
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0016) || !(y <= 7e+61))
		tmp = Float64(x / Float64(y * Float64(a / (z ^ 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 ((y <= -0.0016) || ~((y <= 7e+61)))
		tmp = x / (y * (a / (z ^ y)));
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0016], N[Not[LessEqual[y, 7e+61]], $MachinePrecision]], N[(x / N[(y * N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00160000000000000008 or 7.00000000000000036e61 < y

   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/ 90.0%

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

      2. associate--l+ 90.0%

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

      3. exp-sum 59.7%

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

      4. associate-*r* 59.7%

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

      5. *-commutative 59.7%

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

      6. exp-to-pow 59.7%

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

      7. exp-diff 58.1%

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

      8. *-commutative 58.1%

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

      9. exp-to-pow 58.2%

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

      10. sub-neg 58.2%

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

      11. metadata-eval 58.2%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. *-commutative 65.7%

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

      2. times-frac 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in b around 0 78.0%

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

      1. *-commutative 78.0%

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

      2. clear-num 78.0%

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

      3. frac-times 86.3%

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

      4. *-un-lft-identity 86.3%

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

   9. Applied egg-rr 86.3%

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

   if -0.00160000000000000008 < y < 7.00000000000000036e61

   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/ 90.2%

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

      2. associate--l+ 90.2%

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

      3. exp-sum 87.2%

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

      4. associate-*r* 87.2%

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

      5. *-commutative 87.2%

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

      6. exp-to-pow 87.2%

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

      7. exp-diff 79.0%

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

      8. *-commutative 79.0%

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

      9. exp-to-pow 79.9%

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

      10. sub-neg 79.9%

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

      11. metadata-eval 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in t around 0 67.4%

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

      1. *-commutative 67.4%

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

      2. times-frac 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in y around 0 68.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0016 \lor \neg \left(y \leq 7 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{y \cdot \frac{a}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 72.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -31000000:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -31000000.0)
   (/ x (* a (* y (exp b))))
   (if (<= b 2.6e-24) (* (/ (pow z y) a) (/ x y)) (/ (/ x (* a (exp b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -31000000.0) {
		tmp = x / (a * (y * exp(b)));
	} else if (b <= 2.6e-24) {
		tmp = (pow(z, y) / a) * (x / y);
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-31000000.0d0)) then
        tmp = x / (a * (y * exp(b)))
    else if (b <= 2.6d-24) then
        tmp = ((z ** y) / a) * (x / y)
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -31000000.0) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (b <= 2.6e-24) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -31000000.0:
		tmp = x / (a * (y * math.exp(b)))
	elif b <= 2.6e-24:
		tmp = (math.pow(z, y) / a) * (x / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -31000000.0)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (b <= 2.6e-24)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -31000000.0)
		tmp = x / (a * (y * exp(b)));
	elseif (b <= 2.6e-24)
		tmp = ((z ^ y) / a) * (x / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -31000000.0], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-24], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1e7

   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/ 88.1%

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

      2. associate--l+ 88.1%

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

      3. exp-sum 66.1%

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

      4. associate-*r* 66.1%

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

      5. *-commutative 66.1%

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

      6. exp-to-pow 66.1%

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

      7. exp-diff 50.8%

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

      8. *-commutative 50.8%

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

      9. exp-to-pow 50.8%

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

      10. sub-neg 50.8%

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

      11. metadata-eval 50.8%

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

   3. Simplified 50.8%

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

   4. Taylor expanded in t around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. times-frac 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in y around 0 78.3%

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

   if -3.1e7 < b < 2.6e-24

   1. Initial program 97.8%

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

      1. associate-*l/ 92.5%

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

      2. associate--l+ 92.5%

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

      3. exp-sum 86.1%

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

      4. associate-*r* 86.1%

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

      5. *-commutative 86.1%

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

      6. exp-to-pow 86.1%

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

      7. exp-diff 86.1%

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

      8. *-commutative 86.1%

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

      9. exp-to-pow 87.2%

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

      10. sub-neg 87.2%

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

      11. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. *-commutative 65.7%

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

      2. times-frac 68.2%

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

   6. Simplified 68.2%

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

   7. Taylor expanded in b around 0 68.2%

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

   if 2.6e-24 < 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. Taylor expanded in y around 0 83.6%

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

      1. exp-diff 72.4%

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

      2. exp-to-pow 72.4%

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

      3. sub-neg 72.4%

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

      4. metadata-eval 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in t around 0 78.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -31000000:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 9: 58.7% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.9%

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

   1. associate-*l/ 90.1%

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

   2. associate--l+ 90.1%

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

   3. exp-sum 74.1%

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

   4. associate-*r* 74.1%

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

   5. *-commutative 74.1%

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

   6. exp-to-pow 74.1%

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

   7. exp-diff 69.0%

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

   8. *-commutative 69.0%

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

   9. exp-to-pow 69.5%

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

   10. sub-neg 69.5%

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

   11. metadata-eval 69.5%

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

3. Simplified 69.5%

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

4. Taylor expanded in t around 0 66.5%

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

   1. *-commutative 66.5%

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

   2. times-frac 67.8%

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

6. Simplified 67.8%

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

7. Taylor expanded in y around 0 55.7%

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

8. Final simplification 55.7%

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

Alternative 10: 58.7% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.9%

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

2. Taylor expanded in y around 0 78.1%

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

   1. exp-diff 69.5%

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

   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%

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

4. Simplified 69.9%

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

5. Taylor expanded in t around 0 56.7%

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

6. Final simplification 56.7%

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

Alternative 11: 39.6% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-155}:\\ \;\;\;\;\frac{y \cdot \frac{x}{y} - \frac{a \cdot b}{\frac{a}{x}}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e-155)
   (/ (- (* y (/ x y)) (/ (* a b) (/ a x))) (* y a))
   (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e-155) {
		tmp = ((y * (x / y)) - ((a * b) / (a / x))) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d-155)) then
        tmp = ((y * (x / y)) - ((a * b) / (a / x))) / (y * a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e-155) {
		tmp = ((y * (x / y)) - ((a * b) / (a / x))) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e-155:
		tmp = ((y * (x / y)) - ((a * b) / (a / x))) / (y * a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e-155)
		tmp = Float64(Float64(Float64(y * Float64(x / y)) - Float64(Float64(a * b) / Float64(a / x))) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e-155)
		tmp = ((y * (x / y)) - ((a * b) / (a / x))) / (y * a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e-155], N[(N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * 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 < -9.50000000000000024e-155

   1. Initial program 98.7%

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

      1. associate-*l/ 90.1%

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

      2. associate--l+ 90.1%

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

      3. exp-sum 75.2%

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

      4. associate-*r* 75.2%

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

      5. *-commutative 75.2%

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

      6. exp-to-pow 75.2%

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

      7. exp-diff 65.6%

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

      8. *-commutative 65.6%

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

      9. exp-to-pow 66.0%

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

      10. sub-neg 66.0%

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

      11. metadata-eval 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in t around 0 63.3%

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

      1. *-commutative 63.3%

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

      2. times-frac 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around 0 58.5%

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

   8. Taylor expanded in b around 0 29.7%

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

      1. +-commutative 29.7%

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

      2. mul-1-neg 29.7%

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

      3. unsub-neg 29.7%

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

      4. *-commutative 29.7%

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

      5. *-commutative 29.7%

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

      6. times-frac 28.9%

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

   10. Simplified 28.9%

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

       1. div-inv 28.9%

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

       2. associate-/r* 27.9%

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

       3. associate-*r/ 26.8%

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

       4. frac-sub 31.8%

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

       5. div-inv 31.8%

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

   12. Applied egg-rr 31.8%

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

       1. *-commutative 31.8%

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

       2. associate-*l/ 31.8%

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

       3. *-commutative 31.8%

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

       4. associate-/l* 31.8%

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

       5. associate-*r/ 34.8%

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

       6. *-commutative 34.8%

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

   14. Simplified 34.8%

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

   if -9.50000000000000024e-155 < b

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 76.4%

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

      1. exp-diff 71.5%

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

      2. exp-to-pow 72.0%

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

      3. sub-neg 72.0%

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

      4. metadata-eval 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in t around 0 57.3%

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

   6. Taylor expanded in b around 0 40.9%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-155}:\\ \;\;\;\;\frac{y \cdot \frac{x}{y} - \frac{a \cdot b}{\frac{a}{x}}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 12: 38.4% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -1.58 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+99)
   (/ (* b (- x)) (* y a))
   (if (<= b -1.58e-289)
     (/ x (* y a))
     (if (<= b 1.6e+33) (/ (/ x a) y) (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+99) {
		tmp = (b * -x) / (y * a);
	} else if (b <= -1.58e-289) {
		tmp = x / (y * a);
	} else if (b <= 1.6e+33) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.5d+99)) then
        tmp = (b * -x) / (y * a)
    else if (b <= (-1.58d-289)) then
        tmp = x / (y * a)
    else if (b <= 1.6d+33) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+99) {
		tmp = (b * -x) / (y * a);
	} else if (b <= -1.58e-289) {
		tmp = x / (y * a);
	} else if (b <= 1.6e+33) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+99:
		tmp = (b * -x) / (y * a)
	elif b <= -1.58e-289:
		tmp = x / (y * a)
	elif b <= 1.6e+33:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+99)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(y * a));
	elseif (b <= -1.58e-289)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.6e+33)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+99)
		tmp = (b * -x) / (y * a);
	elseif (b <= -1.58e-289)
		tmp = x / (y * a);
	elseif (b <= 1.6e+33)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+99], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.58e-289], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+33], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.50000000000000004e99

   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/ 89.7%

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

      2. associate--l+ 89.7%

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

      3. exp-sum 69.2%

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

      4. associate-*r* 69.2%

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

      5. *-commutative 69.2%

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

      6. exp-to-pow 69.2%

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

      7. exp-diff 51.3%

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

      8. *-commutative 51.3%

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

      9. exp-to-pow 51.3%

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

      10. sub-neg 51.3%

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

      11. metadata-eval 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. times-frac 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around 0 87.4%

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

   8. Taylor expanded in b around 0 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

      5. *-commutative 42.7%

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

      6. times-frac 35.5%

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

   10. Simplified 35.5%

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

   11. Taylor expanded in b around inf 42.7%

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

       1. neg-mul-1 42.7%

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

       2. distribute-neg-frac 42.7%

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

       3. distribute-rgt-neg-out 42.7%

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

       4. *-commutative 42.7%

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

   13. Simplified 42.7%

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

   if -2.50000000000000004e99 < b < -1.5799999999999999e-289

   1. Initial program 98.0%

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

      1. associate-*l/ 89.2%

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

      2. associate--l+ 89.2%

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

      3. exp-sum 79.1%

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

      4. associate-*r* 79.1%

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

      5. *-commutative 79.1%

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

      6. exp-to-pow 79.1%

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

      7. exp-diff 76.6%

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

      8. *-commutative 76.6%

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

      9. exp-to-pow 77.3%

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

      10. sub-neg 77.3%

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

      11. metadata-eval 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in t around 0 59.1%

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

      1. *-commutative 59.1%

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

      2. times-frac 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in y around 0 39.9%

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

   8. Taylor expanded in b around 0 31.4%

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

      1. *-commutative 31.4%

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

   10. Simplified 31.4%

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

   if -1.5799999999999999e-289 < b < 1.60000000000000009e33

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 69.3%

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

      1. exp-diff 68.0%

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

      2. exp-to-pow 68.8%

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

      3. sub-neg 68.8%

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

      4. metadata-eval 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in t around 0 44.5%

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

   6. Taylor expanded in b around 0 42.0%

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

   if 1.60000000000000009e33 < 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. Taylor expanded in y around 0 83.3%

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

      1. exp-diff 71.3%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in t around 0 81.6%

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

   6. Taylor expanded in b around 0 39.7%

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

   7. Taylor expanded in x around 0 44.4%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -1.58 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 13: 39.1% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.6e+99)
   (/ (- (/ x y) (* x (/ b y))) a)
   (if (<= b 1.52e-297)
     (/ x (* y a))
     (if (<= b 1.05e-232) (/ (/ x (* a b)) y) (/ (/ x (+ a (* a b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+99) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= 1.52e-297) {
		tmp = x / (y * a);
	} else if (b <= 1.05e-232) {
		tmp = (x / (a * b)) / y;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.6d+99)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= 1.52d-297) then
        tmp = x / (y * a)
    else if (b <= 1.05d-232) then
        tmp = (x / (a * b)) / y
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+99) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= 1.52e-297) {
		tmp = x / (y * a);
	} else if (b <= 1.05e-232) {
		tmp = (x / (a * b)) / y;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.6e+99:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= 1.52e-297:
		tmp = x / (y * a)
	elif b <= 1.05e-232:
		tmp = (x / (a * b)) / y
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.6e+99)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= 1.52e-297)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.05e-232)
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.6e+99)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= 1.52e-297)
		tmp = x / (y * a);
	elseif (b <= 1.05e-232)
		tmp = (x / (a * b)) / y;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.6e+99], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.52e-297], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-232], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.6e99

   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/ 89.7%

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

      2. associate--l+ 89.7%

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

      3. exp-sum 69.2%

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

      4. associate-*r* 69.2%

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

      5. *-commutative 69.2%

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

      6. exp-to-pow 69.2%

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

      7. exp-diff 51.3%

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

      8. *-commutative 51.3%

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

      9. exp-to-pow 51.3%

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

      10. sub-neg 51.3%

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

      11. metadata-eval 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. times-frac 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around 0 87.4%

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

   8. Taylor expanded in b around 0 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

      5. *-commutative 42.7%

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

      6. times-frac 35.5%

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

   10. Simplified 35.5%

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

       1. associate-*l/ 45.3%

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

       2. associate-/r* 45.3%

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

       3. sub-div 45.3%

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

   12. Applied egg-rr 45.3%

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

   if -2.6e99 < b < 1.52e-297

   1. Initial program 98.0%

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

      1. associate-*l/ 90.0%

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

      2. associate--l+ 90.0%

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

      3. exp-sum 81.0%

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

      4. associate-*r* 81.0%

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

      5. *-commutative 81.0%

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

      6. exp-to-pow 81.0%

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

      7. exp-diff 78.7%

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

      8. *-commutative 78.7%

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

      9. exp-to-pow 79.6%

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

      10. sub-neg 79.6%

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

      11. metadata-eval 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in t around 0 58.9%

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

      1. *-commutative 58.9%

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

      2. times-frac 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in y around 0 40.5%

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

   8. Taylor expanded in b around 0 32.9%

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

      1. *-commutative 32.9%

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

   10. Simplified 32.9%

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

   if 1.52e-297 < b < 1.05e-232

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 68.8%

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

      1. exp-diff 68.8%

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

      2. exp-to-pow 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in t around 0 27.5%

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

   6. Taylor expanded in b around 0 27.5%

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

   7. Taylor expanded in b around inf 39.1%

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

   if 1.05e-232 < b

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 74.4%

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

      1. exp-diff 67.3%

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

      2. exp-to-pow 67.5%

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

      3. sub-neg 67.5%

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

      4. metadata-eval 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in t around 0 66.2%

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

   6. Taylor expanded in b around 0 42.6%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 14: 38.3% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e+102)
   (/ (* b (- x)) (* y a))
   (if (<= b -7.6e-290)
     (/ x (* y a))
     (if (<= b 1.4e+33) (/ (/ 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 <= -5e+102) {
		tmp = (b * -x) / (y * a);
	} else if (b <= -7.6e-290) {
		tmp = x / (y * a);
	} else if (b <= 1.4e+33) {
		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 <= (-5d+102)) then
        tmp = (b * -x) / (y * a)
    else if (b <= (-7.6d-290)) then
        tmp = x / (y * a)
    else if (b <= 1.4d+33) 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 <= -5e+102) {
		tmp = (b * -x) / (y * a);
	} else if (b <= -7.6e-290) {
		tmp = x / (y * a);
	} else if (b <= 1.4e+33) {
		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 <= -5e+102:
		tmp = (b * -x) / (y * a)
	elif b <= -7.6e-290:
		tmp = x / (y * a)
	elif b <= 1.4e+33:
		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 <= -5e+102)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(y * a));
	elseif (b <= -7.6e-290)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 1.4e+33)
		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 <= -5e+102)
		tmp = (b * -x) / (y * a);
	elseif (b <= -7.6e-290)
		tmp = x / (y * a);
	elseif (b <= 1.4e+33)
		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, -5e+102], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.6e-290], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+33], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5e102

   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/ 89.7%

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

      2. associate--l+ 89.7%

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

      3. exp-sum 69.2%

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

      4. associate-*r* 69.2%

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

      5. *-commutative 69.2%

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

      6. exp-to-pow 69.2%

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

      7. exp-diff 51.3%

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

      8. *-commutative 51.3%

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

      9. exp-to-pow 51.3%

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

      10. sub-neg 51.3%

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

      11. metadata-eval 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. times-frac 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around 0 87.4%

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

   8. Taylor expanded in b around 0 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

      5. *-commutative 42.7%

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

      6. times-frac 35.5%

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

   10. Simplified 35.5%

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

   11. Taylor expanded in b around inf 42.7%

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

       1. neg-mul-1 42.7%

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

       2. distribute-neg-frac 42.7%

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

       3. distribute-rgt-neg-out 42.7%

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

       4. *-commutative 42.7%

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

   13. Simplified 42.7%

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

   if -5e102 < b < -7.5999999999999995e-290

   1. Initial program 98.0%

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

      1. associate-*l/ 89.2%

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

      2. associate--l+ 89.2%

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

      3. exp-sum 79.1%

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

      4. associate-*r* 79.1%

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

      5. *-commutative 79.1%

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

      6. exp-to-pow 79.1%

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

      7. exp-diff 76.6%

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

      8. *-commutative 76.6%

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

      9. exp-to-pow 77.3%

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

      10. sub-neg 77.3%

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

      11. metadata-eval 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in t around 0 59.1%

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

      1. *-commutative 59.1%

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

      2. times-frac 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in y around 0 39.9%

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

   8. Taylor expanded in b around 0 31.4%

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

      1. *-commutative 31.4%

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

   10. Simplified 31.4%

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

   if -7.5999999999999995e-290 < b < 1.4e33

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 69.3%

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

      1. exp-diff 68.0%

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

      2. exp-to-pow 68.8%

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

      3. sub-neg 68.8%

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

      4. metadata-eval 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in t around 0 44.5%

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

   6. Taylor expanded in b around 0 42.0%

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

   if 1.4e33 < 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. Taylor expanded in y around 0 83.3%

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

      1. exp-diff 71.3%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in t around 0 81.6%

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

   6. Taylor expanded in b around 0 39.7%

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

   7. Taylor expanded in b around inf 42.3%

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

      1. *-commutative 42.3%

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

   9. Simplified 42.3%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+102}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 15: 38.6% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.6e+100)
   (/ (* b (- x)) (* y a))
   (if (<= b -8e-284) (/ x (* y a)) (/ (/ x (+ a (* a b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.6e+100) {
		tmp = (b * -x) / (y * a);
	} else if (b <= -8e-284) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.6d+100)) then
        tmp = (b * -x) / (y * a)
    else if (b <= (-8d-284)) then
        tmp = x / (y * a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.6e+100) {
		tmp = (b * -x) / (y * a);
	} else if (b <= -8e-284) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.6e+100:
		tmp = (b * -x) / (y * a)
	elif b <= -8e-284:
		tmp = x / (y * a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.6e+100)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(y * a));
	elseif (b <= -8e-284)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.6e+100)
		tmp = (b * -x) / (y * a);
	elseif (b <= -8e-284)
		tmp = x / (y * a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.6e+100], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8e-284], N[(x / N[(y * a), $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 < -8.59999999999999986e100

   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/ 89.7%

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

      2. associate--l+ 89.7%

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

      3. exp-sum 69.2%

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

      4. associate-*r* 69.2%

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

      5. *-commutative 69.2%

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

      6. exp-to-pow 69.2%

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

      7. exp-diff 51.3%

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

      8. *-commutative 51.3%

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

      9. exp-to-pow 51.3%

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

      10. sub-neg 51.3%

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

      11. metadata-eval 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. times-frac 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around 0 87.4%

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

   8. Taylor expanded in b around 0 42.7%

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

      1. +-commutative 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. *-commutative 42.7%

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

      5. *-commutative 42.7%

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

      6. times-frac 35.5%

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

   10. Simplified 35.5%

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

   11. Taylor expanded in b around inf 42.7%

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

       1. neg-mul-1 42.7%

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

       2. distribute-neg-frac 42.7%

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

       3. distribute-rgt-neg-out 42.7%

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

       4. *-commutative 42.7%

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

   13. Simplified 42.7%

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

   if -8.59999999999999986e100 < b < -8.00000000000000029e-284

   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/ 89.1%

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

      2. associate--l+ 89.1%

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

      3. exp-sum 78.9%

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

      4. associate-*r* 78.9%

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

      5. *-commutative 78.9%

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

      6. exp-to-pow 78.9%

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

      7. exp-diff 76.3%

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

      8. *-commutative 76.3%

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

      9. exp-to-pow 77.0%

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

      10. sub-neg 77.0%

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

      11. metadata-eval 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in t around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. times-frac 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in y around 0 40.2%

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

   8. Taylor expanded in b around 0 31.6%

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

      1. *-commutative 31.6%

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

   10. Simplified 31.6%

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

   if -8.00000000000000029e-284 < b

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 74.9%

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

      1. exp-diff 69.1%

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

      2. exp-to-pow 69.5%

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

      3. sub-neg 69.5%

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

      4. metadata-eval 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in t around 0 60.0%

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

   6. Taylor expanded in b around 0 40.9%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 16: 35.5% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.15e-284)
   (* x (/ 1.0 (* y a)))
   (if (<= b 3.5e+33) (/ (/ 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 <= -2.15e-284) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 3.5e+33) {
		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 <= (-2.15d-284)) then
        tmp = x * (1.0d0 / (y * a))
    else if (b <= 3.5d+33) 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 <= -2.15e-284) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 3.5e+33) {
		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 <= -2.15e-284:
		tmp = x * (1.0 / (y * a))
	elif b <= 3.5e+33:
		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 <= -2.15e-284)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 3.5e+33)
		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 <= -2.15e-284)
		tmp = x * (1.0 / (y * a));
	elseif (b <= 3.5e+33)
		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, -2.15e-284], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+33], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1500000000000001e-284

   1. Initial program 98.8%

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

      1. associate-*l/ 89.3%

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

      2. associate--l+ 89.3%

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

      3. exp-sum 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. exp-to-pow 75.7%

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

      7. exp-diff 68.0%

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

      8. *-commutative 68.0%

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

      9. exp-to-pow 68.4%

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

      10. sub-neg 68.4%

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

      11. metadata-eval 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in t around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. times-frac 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in y around 0 55.9%

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

   8. Taylor expanded in b around 0 24.7%

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

      1. *-commutative 24.7%

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

   10. Simplified 24.7%

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

       1. div-inv 25.4%

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

       2. /-rgt-identity 25.4%

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

       3. clear-num 25.4%

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

       4. div-inv 25.4%

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

       5. div-inv 25.4%

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

       6. clear-num 25.4%

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

       7. /-rgt-identity 25.4%

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

       8. *-commutative 25.4%

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

   12. Applied egg-rr 25.4%

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

   if -2.1500000000000001e-284 < b < 3.5000000000000001e33

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 68.6%

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

      1. exp-diff 67.4%

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

      2. exp-to-pow 68.1%

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

      3. sub-neg 68.1%

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

      4. metadata-eval 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around 0 44.1%

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

   6. Taylor expanded in b around 0 41.7%

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

   if 3.5000000000000001e33 < 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. Taylor expanded in y around 0 83.3%

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

      1. exp-diff 71.3%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in t around 0 81.6%

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

   6. Taylor expanded in b around 0 39.7%

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

   7. Taylor expanded in b around inf 42.3%

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

      1. *-commutative 42.3%

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

   9. Simplified 42.3%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 17: 38.1% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e-154)
   (* x (/ (- b) (* y a)))
   (if (<= b 8.5e+32) (/ (/ 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 <= -3.7e-154) {
		tmp = x * (-b / (y * a));
	} else if (b <= 8.5e+32) {
		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 <= (-3.7d-154)) then
        tmp = x * (-b / (y * a))
    else if (b <= 8.5d+32) 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 <= -3.7e-154) {
		tmp = x * (-b / (y * a));
	} else if (b <= 8.5e+32) {
		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 <= -3.7e-154:
		tmp = x * (-b / (y * a))
	elif b <= 8.5e+32:
		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 <= -3.7e-154)
		tmp = Float64(x * Float64(Float64(-b) / Float64(y * a)));
	elseif (b <= 8.5e+32)
		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 <= -3.7e-154)
		tmp = x * (-b / (y * a));
	elseif (b <= 8.5e+32)
		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, -3.7e-154], N[(x * N[((-b) / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+32], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.69999999999999987e-154

   1. Initial program 98.7%

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

      1. associate-*l/ 90.1%

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

      2. associate--l+ 90.1%

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

      3. exp-sum 75.2%

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

      4. associate-*r* 75.2%

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

      5. *-commutative 75.2%

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

      6. exp-to-pow 75.2%

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

      7. exp-diff 65.6%

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

      8. *-commutative 65.6%

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

      9. exp-to-pow 66.0%

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

      10. sub-neg 66.0%

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

      11. metadata-eval 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in t around 0 63.3%

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

      1. *-commutative 63.3%

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

      2. times-frac 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around 0 58.5%

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

   8. Taylor expanded in b around 0 29.7%

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

      1. +-commutative 29.7%

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

      2. mul-1-neg 29.7%

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

      3. unsub-neg 29.7%

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

      4. *-commutative 29.7%

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

      5. *-commutative 29.7%

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

      6. times-frac 28.9%

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

   10. Simplified 28.9%

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

   11. Taylor expanded in b around inf 26.0%

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

       1. associate-*r/ 26.0%

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

       2. *-commutative 26.0%

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

       3. neg-mul-1 26.0%

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

       4. distribute-rgt-neg-in 26.0%

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

       5. associate-*r/ 28.2%

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

       6. *-commutative 28.2%

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

   13. Simplified 28.2%

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

   if -3.69999999999999987e-154 < b < 8.4999999999999998e32

   1. Initial program 98.5%

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

   2. Taylor expanded in y around 0 72.5%

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

      1. exp-diff 71.5%

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

      2. exp-to-pow 72.4%

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

      3. sub-neg 72.4%

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

      4. metadata-eval 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in t around 0 43.4%

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

   6. Taylor expanded in b around 0 41.5%

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

   if 8.4999999999999998e32 < 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. Taylor expanded in y around 0 83.3%

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

      1. exp-diff 71.3%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in t around 0 81.6%

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

   6. Taylor expanded in b around 0 39.7%

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

   7. Taylor expanded in b around inf 42.3%

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

      1. *-commutative 42.3%

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

   9. Simplified 42.3%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 18: 31.1% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e-280) (* x (/ 1.0 (* y a))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e-280) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.1d-280)) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e-280) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1e-280:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e-280)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e-280)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e-280], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1000000000000001e-280

   1. Initial program 98.8%

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

      1. associate-*l/ 89.3%

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

      2. associate--l+ 89.3%

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

      3. exp-sum 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. exp-to-pow 75.7%

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

      7. exp-diff 68.0%

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

      8. *-commutative 68.0%

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

      9. exp-to-pow 68.4%

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

      10. sub-neg 68.4%

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

      11. metadata-eval 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in t around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. times-frac 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in y around 0 55.9%

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

   8. Taylor expanded in b around 0 24.7%

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

      1. *-commutative 24.7%

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

   10. Simplified 24.7%

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

       1. div-inv 25.4%

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

       2. /-rgt-identity 25.4%

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

       3. clear-num 25.4%

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

       4. div-inv 25.4%

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

       5. div-inv 25.4%

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

       6. clear-num 25.4%

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

       7. /-rgt-identity 25.4%

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

       8. *-commutative 25.4%

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

   12. Applied egg-rr 25.4%

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

   if -1.1000000000000001e-280 < b

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 74.9%

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

      1. exp-diff 69.1%

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

      2. exp-to-pow 69.5%

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

      3. sub-neg 69.5%

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

      4. metadata-eval 69.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 69.5%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 60.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 31.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 19: 31.1% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.5e-278) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e-278) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.5d-278)) then
        tmp = x / (y * a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e-278) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.5e-278:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.5e-278)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.5e-278)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.5e-278], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4999999999999998e-278

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. associate--l+ 89.3%

         \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

      3. exp-sum 75.7%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

      4. associate-*r* 75.7%

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

      5. *-commutative 75.7%

         \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      6. exp-to-pow 75.7%

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

      7. exp-diff 68.0%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

      8. *-commutative 68.0%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

      9. exp-to-pow 68.4%

         \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

      10. sub-neg 68.4%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

      11. metadata-eval 68.4%

          \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

   4. Taylor expanded in t around 0 63.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. *-commutative 63.0%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. times-frac 61.5%

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}} \]

   6. Simplified 61.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}} \]

   7. Taylor expanded in y around 0 55.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 24.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 24.7%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 24.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if -4.4999999999999998e-278 < b

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 74.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. exp-diff 69.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 69.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 69.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 69.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   4. Simplified 69.5%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   5. Taylor expanded in t around 0 60.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   6. Taylor expanded in b around 0 31.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 20: 30.8% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.9%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 90.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. associate--l+ 90.1%

      \[\leadsto \frac{x}{y} \cdot e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \]

   3. exp-sum 74.1%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}\right)} \]

   4. associate-*r* 74.1%

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot e^{y \cdot \log z}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b}} \]

   5. *-commutative 74.1%

      \[\leadsto \left(\frac{x}{y} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

   6. exp-to-pow 74.1%

      \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{{z}^{y}}\right) \cdot e^{\left(t - 1\right) \cdot \log a - b} \]

   7. exp-diff 69.0%

      \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}} \]

   8. *-commutative 69.0%

      \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \]

   9. exp-to-pow 69.5%

      \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}} \]

   10. sub-neg 69.5%

       \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}} \]

   11. metadata-eval 69.5%

       \[\leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}} \]

3. Simplified 69.5%

   \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}} \]

4. Taylor expanded in t around 0 66.5%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
5. Step-by-step derivation

   1. *-commutative 66.5%

      \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

   2. times-frac 67.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}} \]

6. Simplified 67.8%

   \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}} \cdot \frac{{z}^{y}}{a}} \]

7. Taylor expanded in y around 0 55.7%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

8. Taylor expanded in b around 0 26.1%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
9. Step-by-step derivation

   1. *-commutative 26.1%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

10. Simplified 26.1%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

11. Final simplification 26.1%

    \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 71.8% 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 2023340 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))