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

Percentage Accurate: 98.5% → 98.5%

Time: 22.2s

Alternatives: 24

Speedup: 1.0×

• 21.0% 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: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

2. Final simplification 97.7%

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

Alternative 2: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+49} \lor \neg \left(y \leq 1.05 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.12e+49) (not (<= y 1.05e-54)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.12e+49) || !(y <= 1.05e-54)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.12d+49)) .or. (.not. (y <= 1.05d-54))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.12e+49) || !(y <= 1.05e-54)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.12e+49) or not (y <= 1.05e-54):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.12e+49) || !(y <= 1.05e-54))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.12e+49) || ~((y <= 1.05e-54)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.12e+49], N[Not[LessEqual[y, 1.05e-54]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.12000000000000005e49 or 1.05e-54 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. mul-1-neg 91.8%

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

      3. unsub-neg 91.8%

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

   4. Simplified 91.8%

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

   if -1.12000000000000005e49 < y < 1.05e-54

   1. Initial program 96.2%

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

   2. Taylor expanded in y around 0 95.7%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+49} \lor \neg \left(y \leq 1.05 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 80.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := {a}^{\left(t + -1\right)}\\ t_3 := \frac{x}{\frac{y}{{z}^{y} \cdot t_2}}\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{\frac{y}{t_2}}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b)))))
        (t_2 (pow a (+ t -1.0)))
        (t_3 (/ x (/ y (* (pow z y) t_2)))))
   (if (<= b -1.8e+137)
     t_1
     (if (<= b -1.8e+90)
       (/ (* x (/ (pow z y) a)) y)
       (if (<= b -1.65e+44)
         (/ x (/ y t_2))
         (if (<= b -1.05e-85)
           t_3
           (if (<= b -5.5e-163)
             (/ x (/ a (/ (pow z y) y)))
             (if (<= b 2.3e-10) t_3 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = pow(a, (t + -1.0));
	double t_3 = x / (y / (pow(z, y) * t_2));
	double tmp;
	if (b <= -1.8e+137) {
		tmp = t_1;
	} else if (b <= -1.8e+90) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (b <= -1.65e+44) {
		tmp = x / (y / t_2);
	} else if (b <= -1.05e-85) {
		tmp = t_3;
	} else if (b <= -5.5e-163) {
		tmp = x / (a / (pow(z, y) / y));
	} else if (b <= 2.3e-10) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (a * (y * exp(b)))
    t_2 = a ** (t + (-1.0d0))
    t_3 = x / (y / ((z ** y) * t_2))
    if (b <= (-1.8d+137)) then
        tmp = t_1
    else if (b <= (-1.8d+90)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (b <= (-1.65d+44)) then
        tmp = x / (y / t_2)
    else if (b <= (-1.05d-85)) then
        tmp = t_3
    else if (b <= (-5.5d-163)) then
        tmp = x / (a / ((z ** y) / y))
    else if (b <= 2.3d-10) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * Math.exp(b)));
	double t_2 = Math.pow(a, (t + -1.0));
	double t_3 = x / (y / (Math.pow(z, y) * t_2));
	double tmp;
	if (b <= -1.8e+137) {
		tmp = t_1;
	} else if (b <= -1.8e+90) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (b <= -1.65e+44) {
		tmp = x / (y / t_2);
	} else if (b <= -1.05e-85) {
		tmp = t_3;
	} else if (b <= -5.5e-163) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else if (b <= 2.3e-10) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = math.pow(a, (t + -1.0))
	t_3 = x / (y / (math.pow(z, y) * t_2))
	tmp = 0
	if b <= -1.8e+137:
		tmp = t_1
	elif b <= -1.8e+90:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif b <= -1.65e+44:
		tmp = x / (y / t_2)
	elif b <= -1.05e-85:
		tmp = t_3
	elif b <= -5.5e-163:
		tmp = x / (a / (math.pow(z, y) / y))
	elif b <= 2.3e-10:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = a ^ Float64(t + -1.0)
	t_3 = Float64(x / Float64(y / Float64((z ^ y) * t_2)))
	tmp = 0.0
	if (b <= -1.8e+137)
		tmp = t_1;
	elseif (b <= -1.8e+90)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (b <= -1.65e+44)
		tmp = Float64(x / Float64(y / t_2));
	elseif (b <= -1.05e-85)
		tmp = t_3;
	elseif (b <= -5.5e-163)
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	elseif (b <= 2.3e-10)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = a ^ (t + -1.0);
	t_3 = x / (y / ((z ^ y) * t_2));
	tmp = 0.0;
	if (b <= -1.8e+137)
		tmp = t_1;
	elseif (b <= -1.8e+90)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (b <= -1.65e+44)
		tmp = x / (y / t_2);
	elseif (b <= -1.05e-85)
		tmp = t_3;
	elseif (b <= -5.5e-163)
		tmp = x / (a / ((z ^ y) / y));
	elseif (b <= 2.3e-10)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+137], t$95$1, If[LessEqual[b, -1.8e+90], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.65e+44], N[(x / N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-85], t$95$3, If[LessEqual[b, -5.5e-163], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-10], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.8e137 or 2.30000000000000007e-10 < 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. Step-by-step derivation

      1. associate-*l/ 90.3%

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

      2. *-commutative 90.3%

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

      3. +-commutative 90.3%

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

      4. associate--l+ 90.3%

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

      5. exp-sum 66.5%

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

      6. *-commutative 66.5%

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

      7. exp-to-pow 66.7%

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

      8. sub-neg 66.7%

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

      9. metadata-eval 66.7%

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

      10. exp-diff 51.4%

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

      11. *-commutative 51.4%

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

      12. exp-to-pow 51.4%

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

   3. Simplified 51.4%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. times-frac 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in y around 0 84.1%

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

   if -1.8e137 < b < -1.8e90

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in b around 0 91.1%

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

      1. div-exp 91.1%

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

      2. *-commutative 91.1%

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

      3. exp-to-pow 91.1%

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

      4. rem-exp-log 91.1%

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

   7. Simplified 91.1%

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

   if -1.8e90 < b < -1.65000000000000007e44

   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/ 85.7%

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

      2. *-commutative 85.7%

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

      3. +-commutative 85.7%

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

      4. associate--l+ 85.7%

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

      5. exp-sum 57.1%

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

      6. *-commutative 57.1%

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

      7. exp-to-pow 57.1%

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

      8. sub-neg 57.1%

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

      9. metadata-eval 57.1%

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

      10. exp-diff 42.9%

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

      11. *-commutative 42.9%

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

      12. exp-to-pow 42.9%

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

   3. Simplified 42.9%

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

   4. Taylor expanded in b around 0 57.1%

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

      1. associate-/l* 57.1%

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

      2. *-commutative 57.1%

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

      3. exp-to-pow 57.1%

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

      4. *-commutative 57.1%

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

      5. exp-sum 100.0%

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

      6. exp-sum 57.1%

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

      7. *-commutative 57.1%

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

      8. exp-to-pow 57.1%

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

      9. *-commutative 57.1%

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

      10. exp-to-pow 57.1%

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

      11. sub-neg 57.1%

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

      12. metadata-eval 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in y around 0 86.2%

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

      1. exp-to-pow 86.2%

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

   9. Simplified 86.2%

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

   if -1.65000000000000007e44 < b < -1.05e-85 or -5.4999999999999998e-163 < b < 2.30000000000000007e-10

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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. *-commutative 89.2%

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

      3. +-commutative 89.2%

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

      4. associate--l+ 89.2%

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

      5. exp-sum 83.9%

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

      6. *-commutative 83.9%

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

      7. exp-to-pow 85.1%

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

      8. sub-neg 85.1%

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

      9. metadata-eval 85.1%

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

      10. exp-diff 84.3%

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

      11. *-commutative 84.3%

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

      12. exp-to-pow 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in b around 0 90.8%

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

      1. associate-/l* 90.9%

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

      2. *-commutative 90.9%

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

      3. exp-to-pow 90.9%

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

      4. *-commutative 90.9%

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

      5. exp-sum 96.2%

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

      6. exp-sum 90.9%

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

      7. *-commutative 90.9%

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

      8. exp-to-pow 90.9%

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

      9. *-commutative 90.9%

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

      10. exp-to-pow 92.1%

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

      11. sub-neg 92.1%

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

      12. metadata-eval 92.1%

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

   6. Simplified 92.1%

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

   if -1.05e-85 < b < -5.4999999999999998e-163

   1. Initial program 93.5%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

      3. +-commutative 82.3%

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

      4. associate--l+ 82.3%

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

      5. exp-sum 61.3%

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

      6. *-commutative 61.3%

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

      7. exp-to-pow 63.0%

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

      8. sub-neg 63.0%

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

      9. metadata-eval 63.0%

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

      10. exp-diff 63.0%

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

      11. *-commutative 63.0%

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

      12. exp-to-pow 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in b around 0 61.9%

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

      1. associate-/l* 66.5%

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

      2. *-commutative 66.5%

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

      3. exp-to-pow 66.5%

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

      4. *-commutative 66.5%

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

      5. exp-sum 98.1%

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

      6. exp-sum 66.5%

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

      7. *-commutative 66.5%

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

      8. exp-to-pow 66.5%

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

      9. *-commutative 66.5%

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

      10. exp-to-pow 68.4%

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

      11. sub-neg 68.4%

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

      12. metadata-eval 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in t around 0 74.0%

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

      1. associate-/l* 89.8%

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

   9. Simplified 89.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{a}{\frac{{z}^{y}}{y}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot {a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot {a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 4: 87.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ t_2 := \frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y))
        (t_2 (/ x (/ a (/ (pow z y) y)))))
   (if (<= y -1.6e+103)
     t_2
     (if (<= y 1.05e-54)
       t_1
       (if (<= y 9.5e+18)
         (/ (* x (pow z y)) (* a (* y (exp b))))
         (if (<= y 4.9e+85) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	double t_2 = x / (a / (pow(z, y) / y));
	double tmp;
	if (y <= -1.6e+103) {
		tmp = t_2;
	} else if (y <= 1.05e-54) {
		tmp = t_1;
	} else if (y <= 9.5e+18) {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	} else if (y <= 4.9e+85) {
		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((((t + (-1.0d0)) * log(a)) - b))) / y
    t_2 = x / (a / ((z ** y) / y))
    if (y <= (-1.6d+103)) then
        tmp = t_2
    else if (y <= 1.05d-54) then
        tmp = t_1
    else if (y <= 9.5d+18) then
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    else if (y <= 4.9d+85) 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((((t + -1.0) * Math.log(a)) - b))) / y;
	double t_2 = x / (a / (Math.pow(z, y) / y));
	double tmp;
	if (y <= -1.6e+103) {
		tmp = t_2;
	} else if (y <= 1.05e-54) {
		tmp = t_1;
	} else if (y <= 9.5e+18) {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	} else if (y <= 4.9e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	t_2 = x / (a / (math.pow(z, y) / y))
	tmp = 0
	if y <= -1.6e+103:
		tmp = t_2
	elif y <= 1.05e-54:
		tmp = t_1
	elif y <= 9.5e+18:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	elif y <= 4.9e+85:
		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(Float64(t + -1.0) * log(a)) - b))) / y)
	t_2 = Float64(x / Float64(a / Float64((z ^ y) / y)))
	tmp = 0.0
	if (y <= -1.6e+103)
		tmp = t_2;
	elseif (y <= 1.05e-54)
		tmp = t_1;
	elseif (y <= 9.5e+18)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	elseif (y <= 4.9e+85)
		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((((t + -1.0) * log(a)) - b))) / y;
	t_2 = x / (a / ((z ^ y) / y));
	tmp = 0.0;
	if (y <= -1.6e+103)
		tmp = t_2;
	elseif (y <= 1.05e-54)
		tmp = t_1;
	elseif (y <= 9.5e+18)
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	elseif (y <= 4.9e+85)
		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[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+103], t$95$2, If[LessEqual[y, 1.05e-54], t$95$1, If[LessEqual[y, 9.5e+18], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+85], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999996e103 or 4.8999999999999997e85 < 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/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 62.8%

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

      6. *-commutative 62.8%

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

      7. exp-to-pow 62.8%

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

      8. sub-neg 62.8%

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

      9. metadata-eval 62.8%

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

      10. exp-diff 46.5%

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

      11. *-commutative 46.5%

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

      12. exp-to-pow 46.5%

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

   3. Simplified 46.5%

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

   4. Taylor expanded in b around 0 66.4%

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

      1. associate-/l* 66.4%

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

      2. *-commutative 66.4%

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

      3. exp-to-pow 66.4%

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

      4. *-commutative 66.4%

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

      5. exp-sum 92.0%

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

      6. exp-sum 66.4%

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

      7. *-commutative 66.4%

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

      8. exp-to-pow 66.4%

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

      9. *-commutative 66.4%

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

      10. exp-to-pow 66.4%

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

      11. sub-neg 66.4%

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

      12. metadata-eval 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in t around 0 69.9%

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

      1. associate-/l* 87.4%

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

   9. Simplified 87.4%

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

   if -1.59999999999999996e103 < y < 1.05e-54 or 9.5e18 < y < 4.8999999999999997e85

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 92.7%

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

   if 1.05e-54 < y < 9.5e18

   1. Initial program 93.9%

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

      1. associate-*l/ 98.1%

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

      2. *-commutative 98.1%

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

      3. +-commutative 98.1%

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

      4. associate--l+ 98.1%

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

      5. exp-sum 92.8%

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

      6. *-commutative 92.8%

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

      7. exp-to-pow 94.1%

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

      8. sub-neg 94.1%

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

      9. metadata-eval 94.1%

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

      10. exp-diff 94.1%

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

      11. *-commutative 94.1%

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

      12. exp-to-pow 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 99.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \end{array} \]

Alternative 5: 77.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t + -1\right)}\\ t_2 := \frac{t_1}{e^{b}} \cdot \frac{x}{y}\\ t_3 := \frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{\frac{y}{t_1}}\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (+ t -1.0)))
        (t_2 (* (/ t_1 (exp b)) (/ x y)))
        (t_3 (/ x (/ a (/ (pow z y) y)))))
   (if (<= y -2.8e+49)
     t_3
     (if (<= y -9.5e-224)
       t_2
       (if (<= y 1.12e-129) (/ x (/ y t_1)) (if (<= y 160000.0) t_2 t_3))))))

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 = (t_1 / exp(b)) * (x / y);
	double t_3 = x / (a / (pow(z, y) / y));
	double tmp;
	if (y <= -2.8e+49) {
		tmp = t_3;
	} else if (y <= -9.5e-224) {
		tmp = t_2;
	} else if (y <= 1.12e-129) {
		tmp = x / (y / t_1);
	} else if (y <= 160000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a ** (t + (-1.0d0))
    t_2 = (t_1 / exp(b)) * (x / y)
    t_3 = x / (a / ((z ** y) / y))
    if (y <= (-2.8d+49)) then
        tmp = t_3
    else if (y <= (-9.5d-224)) then
        tmp = t_2
    else if (y <= 1.12d-129) then
        tmp = x / (y / t_1)
    else if (y <= 160000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    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 = (t_1 / Math.exp(b)) * (x / y);
	double t_3 = x / (a / (Math.pow(z, y) / y));
	double tmp;
	if (y <= -2.8e+49) {
		tmp = t_3;
	} else if (y <= -9.5e-224) {
		tmp = t_2;
	} else if (y <= 1.12e-129) {
		tmp = x / (y / t_1);
	} else if (y <= 160000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t + -1.0))
	t_2 = (t_1 / math.exp(b)) * (x / y)
	t_3 = x / (a / (math.pow(z, y) / y))
	tmp = 0
	if y <= -2.8e+49:
		tmp = t_3
	elif y <= -9.5e-224:
		tmp = t_2
	elif y <= 1.12e-129:
		tmp = x / (y / t_1)
	elif y <= 160000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t + -1.0)
	t_2 = Float64(Float64(t_1 / exp(b)) * Float64(x / y))
	t_3 = Float64(x / Float64(a / Float64((z ^ y) / y)))
	tmp = 0.0
	if (y <= -2.8e+49)
		tmp = t_3;
	elseif (y <= -9.5e-224)
		tmp = t_2;
	elseif (y <= 1.12e-129)
		tmp = Float64(x / Float64(y / t_1));
	elseif (y <= 160000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t + -1.0);
	t_2 = (t_1 / exp(b)) * (x / y);
	t_3 = x / (a / ((z ^ y) / y));
	tmp = 0.0;
	if (y <= -2.8e+49)
		tmp = t_3;
	elseif (y <= -9.5e-224)
		tmp = t_2;
	elseif (y <= 1.12e-129)
		tmp = x / (y / t_1);
	elseif (y <= 160000.0)
		tmp = t_2;
	else
		tmp = t_3;
	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[(t$95$1 / N[Exp[b], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+49], t$95$3, If[LessEqual[y, -9.5e-224], t$95$2, If[LessEqual[y, 1.12e-129], N[(x / N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e49 or 1.6e5 < 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/ 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. *-commutative 90.0%

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

      3. +-commutative 90.0%

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

      4. associate--l+ 90.0%

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

      5. exp-sum 65.8%

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

      6. *-commutative 65.8%

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

      7. exp-to-pow 65.8%

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

      8. sub-neg 65.8%

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

      9. metadata-eval 65.8%

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

      10. exp-diff 50.0%

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

      11. *-commutative 50.0%

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

      12. exp-to-pow 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in b around 0 65.1%

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

      1. associate-/l* 65.1%

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

      2. *-commutative 65.1%

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

      3. exp-to-pow 65.1%

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

      4. *-commutative 65.1%

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

      5. exp-sum 89.3%

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

      6. exp-sum 65.1%

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

      7. *-commutative 65.1%

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

      8. exp-to-pow 65.1%

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

      9. *-commutative 65.1%

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

      10. exp-to-pow 65.1%

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

      11. sub-neg 65.1%

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

      12. metadata-eval 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in t around 0 67.7%

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

      1. associate-/l* 82.8%

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

   9. Simplified 82.8%

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

   if -2.7999999999999998e49 < y < -9.5000000000000003e-224 or 1.12000000000000006e-129 < y < 1.6e5

   1. Initial program 96.2%

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

      1. associate-*l/ 94.6%

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

      2. *-commutative 94.6%

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

      3. +-commutative 94.6%

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

      4. associate--l+ 94.6%

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

      5. exp-sum 85.7%

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

      6. *-commutative 85.7%

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

      7. exp-to-pow 87.1%

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

      8. sub-neg 87.1%

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

      9. metadata-eval 87.1%

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

      10. exp-diff 84.5%

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

      11. *-commutative 84.5%

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

      12. exp-to-pow 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in y around 0 87.8%

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

      1. *-commutative 87.8%

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

      2. *-commutative 87.8%

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

      3. times-frac 86.2%

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

      4. exp-to-pow 87.5%

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

      5. sub-neg 87.5%

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

      6. metadata-eval 87.5%

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

   6. Simplified 87.5%

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

   if -9.5000000000000003e-224 < y < 1.12000000000000006e-129

   1. Initial program 95.1%

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

      1. associate-*l/ 79.9%

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

      2. *-commutative 79.9%

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

      3. +-commutative 79.9%

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

      4. associate--l+ 79.9%

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

      5. exp-sum 69.5%

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

      6. *-commutative 69.5%

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

      7. exp-to-pow 70.8%

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

      8. sub-neg 70.8%

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

      9. metadata-eval 70.8%

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

      10. exp-diff 70.8%

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

      11. *-commutative 70.8%

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

      12. exp-to-pow 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in b around 0 80.4%

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

      1. associate-/l* 77.1%

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

      2. *-commutative 77.1%

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

      3. exp-to-pow 77.1%

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

      4. *-commutative 77.1%

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

      5. exp-sum 77.1%

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

      6. exp-sum 77.1%

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

      7. *-commutative 77.1%

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

      8. exp-to-pow 77.1%

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

      9. *-commutative 77.1%

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

      10. exp-to-pow 78.5%

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

      11. sub-neg 78.5%

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

      12. metadata-eval 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in y around 0 77.1%

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

      1. exp-to-pow 78.5%

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

   9. Simplified 78.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \end{array} \]

Alternative 6: 81.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -5e+67) (not (<= (+ t -1.0) -0.5)))
   (/ x (/ y (pow a (+ t -1.0))))
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+67) || !((t + -1.0) <= -0.5)) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-5d+67)) .or. (.not. ((t + (-1.0d0)) <= (-0.5d0)))) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+67) || !((t + -1.0) <= -0.5)) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -5e+67) or not ((t + -1.0) <= -0.5):
		tmp = x / (y / math.pow(a, (t + -1.0)))
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -5e+67) || !(Float64(t + -1.0) <= -0.5))
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -5e+67) || ~(((t + -1.0) <= -0.5)))
		tmp = x / (y / (a ^ (t + -1.0)));
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+67], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -4.99999999999999976e67 or -0.5 < (-.f64 t 1)

   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/ 90.5%

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

      2. *-commutative 90.5%

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

      3. +-commutative 90.5%

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

      4. associate--l+ 90.5%

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

      5. exp-sum 55.2%

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

      6. *-commutative 55.2%

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

      7. exp-to-pow 55.2%

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

      8. sub-neg 55.2%

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

      9. metadata-eval 55.2%

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

      10. exp-diff 50.5%

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

      11. *-commutative 50.5%

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

      12. exp-to-pow 50.5%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in b around 0 62.9%

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

      1. associate-/l* 62.9%

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

      2. *-commutative 62.9%

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

      3. exp-to-pow 62.9%

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

      4. *-commutative 62.9%

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

      5. exp-sum 89.7%

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

      6. exp-sum 62.9%

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

      7. *-commutative 62.9%

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

      8. exp-to-pow 62.9%

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

      9. *-commutative 62.9%

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

      10. exp-to-pow 62.9%

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

      11. sub-neg 62.9%

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

      12. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in y around 0 78.4%

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

      1. exp-to-pow 78.4%

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

   9. Simplified 78.4%

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

   if -4.99999999999999976e67 < (-.f64 t 1) < -0.5

   1. Initial program 96.2%

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

      1. associate-*l/ 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. *-commutative 88.1%

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

      3. +-commutative 88.1%

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

      4. associate--l+ 88.1%

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

      5. exp-sum 84.9%

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

      6. *-commutative 84.9%

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

      7. exp-to-pow 86.1%

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

      8. sub-neg 86.1%

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

      9. metadata-eval 86.1%

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

      10. exp-diff 75.5%

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

      11. *-commutative 75.5%

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

      12. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around 0 84.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 7: 74.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+137} \lor \neg \left(b \leq 5.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.8e+137) (not (<= b 5.2e-10)))
   (/ x (* a (* y (exp b))))
   (/ x (/ a (/ (pow z y) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.8e+137) || !(b <= 5.2e-10)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x / (a / (pow(z, y) / 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 <= (-1.8d+137)) .or. (.not. (b <= 5.2d-10))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x / (a / ((z ** y) / 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 <= -1.8e+137) || !(b <= 5.2e-10)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x / (a / (Math.pow(z, y) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.8e+137) or not (b <= 5.2e-10):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x / (a / (math.pow(z, y) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.8e+137) || !(b <= 5.2e-10))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.8e+137) || ~((b <= 5.2e-10)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x / (a / ((z ^ y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.8e+137], N[Not[LessEqual[b, 5.2e-10]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8e137 or 5.19999999999999962e-10 < 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. 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. *-commutative 90.2%

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

      3. +-commutative 90.2%

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

      4. associate--l+ 90.2%

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

      5. exp-sum 67.2%

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

      6. *-commutative 67.2%

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

      7. exp-to-pow 67.3%

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

      8. sub-neg 67.3%

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

      9. metadata-eval 67.3%

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

      10. exp-diff 51.9%

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

      11. *-commutative 51.9%

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

      12. exp-to-pow 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around 0 70.3%

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

      1. times-frac 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in y around 0 84.8%

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

   if -1.8e137 < b < 5.19999999999999962e-10

   1. Initial program 96.8%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

      3. +-commutative 88.3%

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

      4. associate--l+ 88.3%

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

      5. exp-sum 76.5%

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

      6. *-commutative 76.5%

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

      7. exp-to-pow 77.6%

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

      8. sub-neg 77.6%

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

      9. metadata-eval 77.6%

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

      10. exp-diff 74.4%

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

      11. *-commutative 74.4%

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

      12. exp-to-pow 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in b around 0 83.1%

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

      1. associate-/l* 83.7%

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

      2. *-commutative 83.7%

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

      3. exp-to-pow 83.7%

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

      4. *-commutative 83.7%

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

      5. exp-sum 96.2%

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

      6. exp-sum 83.7%

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

      7. *-commutative 83.7%

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

      8. exp-to-pow 83.7%

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

      9. *-commutative 83.7%

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

      10. exp-to-pow 84.9%

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

      11. sub-neg 84.9%

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

      12. metadata-eval 84.9%

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

   6. Simplified 84.9%

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

   7. Taylor expanded in t around 0 69.7%

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

      1. associate-/l* 77.0%

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

   9. Simplified 77.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+137} \lor \neg \left(b \leq 5.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \end{array} \]

Alternative 8: 58.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.02 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.02e+186)
   (/ x (* a (* y (exp b))))
   (/ (* x 2.0) (* y (* a (* b b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.02e+186) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x * 2.0) / (y * (a * (b * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.02d+186) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x * 2.0d0) / (y * (a * (b * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.02e+186) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * 2.0) / (y * (a * (b * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.02e+186:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x * 2.0) / (y * (a * (b * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.02e+186)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.02e+186)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x * 2.0) / (y * (a * (b * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.02e+186], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.01999999999999999e186

   1. Initial program 97.5%

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

      1. associate-*l/ 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. *-commutative 90.0%

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

      3. +-commutative 90.0%

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

      4. associate--l+ 90.0%

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

      5. exp-sum 74.7%

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

      6. *-commutative 74.7%

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

      7. exp-to-pow 75.5%

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

      8. sub-neg 75.5%

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

      9. metadata-eval 75.5%

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

      10. exp-diff 67.7%

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

      11. *-commutative 67.7%

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

      12. exp-to-pow 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around 0 70.3%

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

      1. times-frac 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in y around 0 66.6%

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

   if 1.01999999999999999e186 < 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/ 81.5%

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

      2. *-commutative 81.5%

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

      3. +-commutative 81.5%

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

      4. associate--l+ 81.5%

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

      5. exp-sum 55.6%

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

      6. *-commutative 55.6%

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

      7. exp-to-pow 55.6%

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

      8. sub-neg 55.6%

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

      9. metadata-eval 55.6%

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

      10. exp-diff 44.4%

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

      11. *-commutative 44.4%

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

      12. exp-to-pow 44.4%

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

   3. Simplified 44.4%

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

   4. Taylor expanded in t around 0 55.6%

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

      1. times-frac 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in y around 0 20.3%

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

   8. Taylor expanded in b around 0 16.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 16.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 16.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 34.9%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 34.9%

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

   10. Simplified 34.9%

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

   11. Taylor expanded in b around inf 45.7%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 45.7%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 45.7%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 42.2%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 42.2%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.02 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \end{array} \]

Alternative 9: 45.8% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + \left(b \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y (* a (* b b))))))
   (if (<= b -3.8e-146)
     (- (/ x (* y a)) (* (/ x a) (/ b y)))
     (if (<= b -5.5e-248)
       t_1
       (if (<= b -5.8e-289)
         (/ x (/ y (- (/ 1.0 a) (/ b a))))
         (if (<= b 7e-240)
           t_1
           (/ x (* a (+ y (* y (+ b (* (* b b) 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -3.8e-146) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= -5.5e-248) {
		tmp = t_1;
	} else if (b <= -5.8e-289) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if (b <= 7e-240) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * (a * (b * b)))
    if (b <= (-3.8d-146)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= (-5.5d-248)) then
        tmp = t_1
    else if (b <= (-5.8d-289)) then
        tmp = x / (y / ((1.0d0 / a) - (b / a)))
    else if (b <= 7d-240) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * (b + ((b * b) * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -3.8e-146) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= -5.5e-248) {
		tmp = t_1;
	} else if (b <= -5.8e-289) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if (b <= 7e-240) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) / (y * (a * (b * b)))
	tmp = 0
	if b <= -3.8e-146:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= -5.5e-248:
		tmp = t_1
	elif b <= -5.8e-289:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	elif b <= 7e-240:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))))
	tmp = 0.0
	if (b <= -3.8e-146)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= -5.5e-248)
		tmp = t_1;
	elseif (b <= -5.8e-289)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))));
	elseif (b <= 7e-240)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b + Float64(Float64(b * b) * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) / (y * (a * (b * b)));
	tmp = 0.0;
	if (b <= -3.8e-146)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= -5.5e-248)
		tmp = t_1;
	elseif (b <= -5.8e-289)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	elseif (b <= 7e-240)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e-146], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-248], t$95$1, If[LessEqual[b, -5.8e-289], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-240], t$95$1, N[(x / N[(a * N[(y + N[(y * N[(b + N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.79999999999999994e-146

   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/ 89.5%

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

      2. *-commutative 89.5%

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

      3. +-commutative 89.5%

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

      4. associate--l+ 89.5%

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

      5. exp-sum 67.9%

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

      6. *-commutative 67.9%

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

      7. exp-to-pow 68.6%

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

      8. sub-neg 68.6%

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

      9. metadata-eval 68.6%

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

      10. exp-diff 58.9%

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

      11. *-commutative 58.9%

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

      12. exp-to-pow 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around 0 66.6%

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

      1. times-frac 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in b around 0 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

      5. *-commutative 52.2%

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

      6. times-frac 55.7%

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

   10. Simplified 55.7%

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

   if -3.79999999999999994e-146 < b < -5.49999999999999979e-248 or -5.80000000000000012e-289 < b < 7.00000000000000032e-240

   1. Initial program 96.7%

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

      1. associate-*l/ 90.7%

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

      2. *-commutative 90.7%

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

      3. +-commutative 90.7%

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

      4. associate--l+ 90.7%

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

      5. exp-sum 78.9%

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

      6. *-commutative 78.9%

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

      7. exp-to-pow 79.5%

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

      8. sub-neg 79.5%

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

      9. metadata-eval 79.5%

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

      10. exp-diff 79.5%

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

      11. *-commutative 79.5%

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

      12. exp-to-pow 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around 0 62.4%

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

      1. times-frac 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 31.3%

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

   8. Taylor expanded in b around 0 31.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 31.3%

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

   10. Simplified 31.3%

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

   11. Taylor expanded in b around inf 59.7%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 59.7%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 59.7%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 59.7%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 59.7%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   if -5.49999999999999979e-248 < b < -5.80000000000000012e-289

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 51.6%

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

      1. exp-neg 51.6%

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

      2. associate-*r/ 51.6%

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

      3. *-rgt-identity 51.6%

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

      4. +-commutative 51.6%

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

      5. exp-sum 51.6%

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

      6. rem-exp-log 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in b around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. associate-/l* 53.1%

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

   10. Simplified 53.1%

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

   11. Taylor expanded in x around 0 53.2%

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

       1. associate-/l* 57.8%

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

   13. Simplified 57.8%

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

   if 7.00000000000000032e-240 < b

   1. Initial program 97.7%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 73.3%

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

      6. *-commutative 73.3%

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

      7. exp-to-pow 74.0%

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

      8. sub-neg 74.0%

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

      9. metadata-eval 74.0%

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

      10. exp-diff 63.1%

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

      11. *-commutative 63.1%

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

      12. exp-to-pow 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. times-frac 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in y around 0 69.9%

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

   8. Taylor expanded in b around 0 56.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 56.4%

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

   10. Simplified 56.4%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + \left(b \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \]

Alternative 10: 49.0% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(b \cdot \left(b \cdot 0.5\right)\right) + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + \left(b \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y (* a (* b b))))))
   (if (<= b -5.8e-144)
     (+ (* (/ x (* y a)) (* b (* b 0.5))) (/ (- x (* x b)) (* y a)))
     (if (<= b -9e-249)
       t_1
       (if (<= b -3e-289)
         (/ x (/ y (- (/ 1.0 a) (/ b a))))
         (if (<= b 1.62e-240)
           t_1
           (/ x (* a (+ y (* y (+ b (* (* b b) 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -5.8e-144) {
		tmp = ((x / (y * a)) * (b * (b * 0.5))) + ((x - (x * b)) / (y * a));
	} else if (b <= -9e-249) {
		tmp = t_1;
	} else if (b <= -3e-289) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if (b <= 1.62e-240) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * (a * (b * b)))
    if (b <= (-5.8d-144)) then
        tmp = ((x / (y * a)) * (b * (b * 0.5d0))) + ((x - (x * b)) / (y * a))
    else if (b <= (-9d-249)) then
        tmp = t_1
    else if (b <= (-3d-289)) then
        tmp = x / (y / ((1.0d0 / a) - (b / a)))
    else if (b <= 1.62d-240) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * (b + ((b * b) * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -5.8e-144) {
		tmp = ((x / (y * a)) * (b * (b * 0.5))) + ((x - (x * b)) / (y * a));
	} else if (b <= -9e-249) {
		tmp = t_1;
	} else if (b <= -3e-289) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if (b <= 1.62e-240) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) / (y * (a * (b * b)))
	tmp = 0
	if b <= -5.8e-144:
		tmp = ((x / (y * a)) * (b * (b * 0.5))) + ((x - (x * b)) / (y * a))
	elif b <= -9e-249:
		tmp = t_1
	elif b <= -3e-289:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	elif b <= 1.62e-240:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))))
	tmp = 0.0
	if (b <= -5.8e-144)
		tmp = Float64(Float64(Float64(x / Float64(y * a)) * Float64(b * Float64(b * 0.5))) + Float64(Float64(x - Float64(x * b)) / Float64(y * a)));
	elseif (b <= -9e-249)
		tmp = t_1;
	elseif (b <= -3e-289)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))));
	elseif (b <= 1.62e-240)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b + Float64(Float64(b * b) * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) / (y * (a * (b * b)));
	tmp = 0.0;
	if (b <= -5.8e-144)
		tmp = ((x / (y * a)) * (b * (b * 0.5))) + ((x - (x * b)) / (y * a));
	elseif (b <= -9e-249)
		tmp = t_1;
	elseif (b <= -3e-289)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	elseif (b <= 1.62e-240)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e-144], N[(N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-249], t$95$1, If[LessEqual[b, -3e-289], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.62e-240], t$95$1, N[(x / N[(a * N[(y + N[(y * N[(b + N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.8000000000000004e-144

   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/ 89.5%

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

      2. *-commutative 89.5%

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

      3. +-commutative 89.5%

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

      4. associate--l+ 89.5%

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

      5. exp-sum 67.9%

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

      6. *-commutative 67.9%

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

      7. exp-to-pow 68.6%

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

      8. sub-neg 68.6%

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

      9. metadata-eval 68.6%

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

      10. exp-diff 58.9%

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

      11. *-commutative 58.9%

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

      12. exp-to-pow 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around 0 66.6%

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

      1. times-frac 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in b around 0 28.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 28.1%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 28.1%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 36.7%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 36.7%

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

   10. Simplified 36.7%

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

   11. Taylor expanded in b around 0 36.1%

       \[\leadsto \color{blue}{-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right)} \]
   12. Step-by-step derivation

   13. Simplified 57.9%

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

   if -5.8000000000000004e-144 < b < -8.99999999999999962e-249 or -2.9999999999999998e-289 < b < 1.61999999999999995e-240

   1. Initial program 96.7%

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

      1. associate-*l/ 90.7%

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

      2. *-commutative 90.7%

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

      3. +-commutative 90.7%

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

      4. associate--l+ 90.7%

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

      5. exp-sum 78.9%

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

      6. *-commutative 78.9%

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

      7. exp-to-pow 79.5%

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

      8. sub-neg 79.5%

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

      9. metadata-eval 79.5%

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

      10. exp-diff 79.5%

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

      11. *-commutative 79.5%

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

      12. exp-to-pow 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around 0 62.4%

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

      1. times-frac 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 31.3%

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

   8. Taylor expanded in b around 0 31.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 31.3%

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

   10. Simplified 31.3%

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

   11. Taylor expanded in b around inf 59.7%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 59.7%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 59.7%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 59.7%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 59.7%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   if -8.99999999999999962e-249 < b < -2.9999999999999998e-289

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 51.6%

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

      1. exp-neg 51.6%

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

      2. associate-*r/ 51.6%

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

      3. *-rgt-identity 51.6%

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

      4. +-commutative 51.6%

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

      5. exp-sum 51.6%

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

      6. rem-exp-log 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in b around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. associate-/l* 53.1%

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

   10. Simplified 53.1%

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

   11. Taylor expanded in x around 0 53.2%

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

       1. associate-/l* 57.8%

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

   13. Simplified 57.8%

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

   if 1.61999999999999995e-240 < b

   1. Initial program 97.7%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 73.3%

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

      6. *-commutative 73.3%

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

      7. exp-to-pow 74.0%

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

      8. sub-neg 74.0%

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

      9. metadata-eval 74.0%

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

      10. exp-diff 63.1%

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

      11. *-commutative 63.1%

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

      12. exp-to-pow 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. times-frac 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in y around 0 69.9%

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

   8. Taylor expanded in b around 0 56.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 56.4%

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

   10. Simplified 56.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(b \cdot \left(b \cdot 0.5\right)\right) + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-249}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + \left(b \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \]

Alternative 11: 49.1% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-115}:\\ \;\;\;\;\frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + \left(b \cdot b\right) \cdot \left(\frac{x}{a} \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 10^{-149}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + \left(b \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e-115)
   (/ (+ (- (/ x a) (/ b (/ a x))) (* (* b b) (* (/ x a) 0.5))) y)
   (if (<= b -1e-248)
     (/ (* x 2.0) (* y (* a (* b b))))
     (if (<= b 1e-149)
       (/ (* x (/ 1.0 a)) y)
       (/ x (* a (+ y (* y (+ b (* (* b b) 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e-115) {
		tmp = (((x / a) - (b / (a / x))) + ((b * b) * ((x / a) * 0.5))) / y;
	} else if (b <= -1e-248) {
		tmp = (x * 2.0) / (y * (a * (b * b)));
	} else if (b <= 1e-149) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.8d-115)) then
        tmp = (((x / a) - (b / (a / x))) + ((b * b) * ((x / a) * 0.5d0))) / y
    else if (b <= (-1d-248)) then
        tmp = (x * 2.0d0) / (y * (a * (b * b)))
    else if (b <= 1d-149) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x / (a * (y + (y * (b + ((b * b) * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e-115) {
		tmp = (((x / a) - (b / (a / x))) + ((b * b) * ((x / a) * 0.5))) / y;
	} else if (b <= -1e-248) {
		tmp = (x * 2.0) / (y * (a * (b * b)));
	} else if (b <= 1e-149) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e-115:
		tmp = (((x / a) - (b / (a / x))) + ((b * b) * ((x / a) * 0.5))) / y
	elif b <= -1e-248:
		tmp = (x * 2.0) / (y * (a * (b * b)))
	elif b <= 1e-149:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e-115)
		tmp = Float64(Float64(Float64(Float64(x / a) - Float64(b / Float64(a / x))) + Float64(Float64(b * b) * Float64(Float64(x / a) * 0.5))) / y);
	elseif (b <= -1e-248)
		tmp = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))));
	elseif (b <= 1e-149)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b + Float64(Float64(b * b) * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e-115)
		tmp = (((x / a) - (b / (a / x))) + ((b * b) * ((x / a) * 0.5))) / y;
	elseif (b <= -1e-248)
		tmp = (x * 2.0) / (y * (a * (b * b)));
	elseif (b <= 1e-149)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x / (a * (y + (y * (b + ((b * b) * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e-115], N[(N[(N[(N[(x / a), $MachinePrecision] - N[(b / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] * N[(N[(x / a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1e-248], N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-149], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * N[(b + N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.7999999999999996e-115

   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 t around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in y around 0 67.6%

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

      1. exp-neg 67.6%

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

      2. associate-*r/ 67.6%

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

      3. *-rgt-identity 67.6%

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

      4. +-commutative 67.6%

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

      5. exp-sum 67.7%

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

      6. rem-exp-log 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in b around 0 49.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}\right)}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}}{y} \]

      2. +-commutative 49.2%

         \[\leadsto \frac{\color{blue}{\left(\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}{y} \]

      3. mul-1-neg 49.2%

         \[\leadsto \frac{\left(\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}{y} \]

      4. unsub-neg 49.2%

         \[\leadsto \frac{\color{blue}{\left(\frac{x}{a} - \frac{b \cdot x}{a}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}{y} \]

      5. associate-/l* 49.2%

         \[\leadsto \frac{\left(\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}{y} \]

      6. mul-1-neg 49.2%

         \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + \color{blue}{\left(-{b}^{2} \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}}{y} \]

      7. distribute-rgt-neg-in 49.2%

         \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + \color{blue}{{b}^{2} \cdot \left(-\left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right)}}{y} \]

      8. distribute-rgt-out 65.4%

         \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + {b}^{2} \cdot \left(-\color{blue}{\frac{x}{a} \cdot \left(-1 + 0.5\right)}\right)}{y} \]

      9. metadata-eval 65.4%

         \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + {b}^{2} \cdot \left(-\frac{x}{a} \cdot \color{blue}{-0.5}\right)}{y} \]

      10. *-commutative 65.4%

          \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + {b}^{2} \cdot \left(-\color{blue}{-0.5 \cdot \frac{x}{a}}\right)}{y} \]

      11. distribute-lft-neg-in 65.4%

          \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + {b}^{2} \cdot \color{blue}{\left(\left(--0.5\right) \cdot \frac{x}{a}\right)}}{y} \]

      12. metadata-eval 65.4%

          \[\leadsto \frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + {b}^{2} \cdot \left(\color{blue}{0.5} \cdot \frac{x}{a}\right)}{y} \]

      13. unpow2 65.4%

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

   10. Simplified 65.4%

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

   if -6.7999999999999996e-115 < b < -9.9999999999999998e-249

   1. Initial program 91.9%

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

      1. associate-*l/ 86.7%

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

      2. *-commutative 86.7%

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

      3. +-commutative 86.7%

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

      4. associate--l+ 86.7%

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

      5. exp-sum 70.7%

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

      6. *-commutative 70.7%

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

      7. exp-to-pow 71.8%

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

      8. sub-neg 71.8%

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

      9. metadata-eval 71.8%

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

      10. exp-diff 71.8%

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

      11. *-commutative 71.8%

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

      12. exp-to-pow 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in t around 0 68.5%

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

      1. times-frac 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in y around 0 33.8%

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

   8. Taylor expanded in b around 0 33.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 33.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 33.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 33.8%

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

   10. Simplified 33.8%

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

   11. Taylor expanded in b around inf 49.1%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 49.1%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 49.1%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 49.1%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 49.1%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   if -9.9999999999999998e-249 < b < 9.99999999999999979e-150

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in b around 0 79.9%

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

      1. div-exp 79.9%

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

      2. *-commutative 79.9%

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

      3. exp-to-pow 79.9%

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

      4. rem-exp-log 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in y around 0 52.2%

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

   if 9.99999999999999979e-150 < b

   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/ 87.9%

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

      2. *-commutative 87.9%

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

      3. +-commutative 87.9%

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

      4. associate--l+ 87.9%

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

      5. exp-sum 71.5%

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

      6. *-commutative 71.5%

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

      7. exp-to-pow 71.9%

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

      8. sub-neg 71.9%

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

      9. metadata-eval 71.9%

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

      10. exp-diff 59.3%

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

      11. *-commutative 59.3%

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

      12. exp-to-pow 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in t around 0 71.1%

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

      1. times-frac 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around 0 72.6%

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

   8. Taylor expanded in b around 0 57.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 57.0%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 57.0%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 57.0%

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

   10. Simplified 57.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-115}:\\ \;\;\;\;\frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + \left(b \cdot b\right) \cdot \left(\frac{x}{a} \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 10^{-149}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + \left(b \cdot b\right) \cdot 0.5\right)\right)}\\ \end{array} \]

Alternative 12: 46.7% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ t_2 := \frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-241} \lor \neg \left(b \leq 0.82\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y (* a (* b b)))))
        (t_2 (/ x (/ y (- (/ 1.0 a) (/ b a))))))
   (if (<= b -1.8e-144)
     t_2
     (if (<= b -3.5e-248)
       t_1
       (if (<= b -5.2e-289)
         t_2
         (if (or (<= b 9.6e-241) (not (<= b 0.82)))
           t_1
           (/ (/ x (+ a (* a b))) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double t_2 = x / (y / ((1.0 / a) - (b / a)));
	double tmp;
	if (b <= -1.8e-144) {
		tmp = t_2;
	} else if (b <= -3.5e-248) {
		tmp = t_1;
	} else if (b <= -5.2e-289) {
		tmp = t_2;
	} else if ((b <= 9.6e-241) || !(b <= 0.82)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * (a * (b * b)))
    t_2 = x / (y / ((1.0d0 / a) - (b / a)))
    if (b <= (-1.8d-144)) then
        tmp = t_2
    else if (b <= (-3.5d-248)) then
        tmp = t_1
    else if (b <= (-5.2d-289)) then
        tmp = t_2
    else if ((b <= 9.6d-241) .or. (.not. (b <= 0.82d0))) then
        tmp = t_1
    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 t_1 = (x * 2.0) / (y * (a * (b * b)));
	double t_2 = x / (y / ((1.0 / a) - (b / a)));
	double tmp;
	if (b <= -1.8e-144) {
		tmp = t_2;
	} else if (b <= -3.5e-248) {
		tmp = t_1;
	} else if (b <= -5.2e-289) {
		tmp = t_2;
	} else if ((b <= 9.6e-241) || !(b <= 0.82)) {
		tmp = t_1;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) / (y * (a * (b * b)))
	t_2 = x / (y / ((1.0 / a) - (b / a)))
	tmp = 0
	if b <= -1.8e-144:
		tmp = t_2
	elif b <= -3.5e-248:
		tmp = t_1
	elif b <= -5.2e-289:
		tmp = t_2
	elif (b <= 9.6e-241) or not (b <= 0.82):
		tmp = t_1
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))))
	t_2 = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))))
	tmp = 0.0
	if (b <= -1.8e-144)
		tmp = t_2;
	elseif (b <= -3.5e-248)
		tmp = t_1;
	elseif (b <= -5.2e-289)
		tmp = t_2;
	elseif ((b <= 9.6e-241) || !(b <= 0.82))
		tmp = t_1;
	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)
	t_1 = (x * 2.0) / (y * (a * (b * b)));
	t_2 = x / (y / ((1.0 / a) - (b / a)));
	tmp = 0.0;
	if (b <= -1.8e-144)
		tmp = t_2;
	elseif (b <= -3.5e-248)
		tmp = t_1;
	elseif (b <= -5.2e-289)
		tmp = t_2;
	elseif ((b <= 9.6e-241) || ~((b <= 0.82)))
		tmp = t_1;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e-144], t$95$2, If[LessEqual[b, -3.5e-248], t$95$1, If[LessEqual[b, -5.2e-289], t$95$2, If[Or[LessEqual[b, 9.6e-241], N[Not[LessEqual[b, 0.82]], $MachinePrecision]], t$95$1, N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8e-144 or -3.49999999999999983e-248 < b < -5.1999999999999998e-289

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. exp-neg 60.6%

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

      2. associate-*r/ 60.6%

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

      3. *-rgt-identity 60.6%

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

      4. +-commutative 60.6%

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

      5. exp-sum 60.7%

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

      6. rem-exp-log 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in b around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. associate-/l* 51.5%

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

   10. Simplified 51.5%

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

   11. Taylor expanded in x around 0 52.4%

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

       1. associate-/l* 55.1%

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

   13. Simplified 55.1%

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

   if -1.8e-144 < b < -3.49999999999999983e-248 or -5.1999999999999998e-289 < b < 9.6e-241 or 0.819999999999999951 < b

   1. Initial program 99.0%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. +-commutative 88.7%

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

      4. associate--l+ 88.7%

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

      5. exp-sum 70.2%

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

      6. *-commutative 70.2%

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

      7. exp-to-pow 70.4%

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

      8. sub-neg 70.4%

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

      9. metadata-eval 70.4%

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

      10. exp-diff 58.4%

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

      11. *-commutative 58.4%

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

      12. exp-to-pow 58.4%

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

   3. Simplified 58.4%

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

   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. times-frac 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in y around 0 66.5%

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

   8. Taylor expanded in b around 0 52.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 52.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 52.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 52.2%

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

   10. Simplified 52.2%

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

   11. Taylor expanded in b around inf 61.2%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 61.2%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 61.2%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 60.3%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 60.3%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   if 9.6e-241 < b < 0.819999999999999951

   1. Initial program 94.0%

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

   2. Taylor expanded in t around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

   4. Simplified 74.7%

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

   5. Taylor expanded in y around 0 49.1%

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

      1. exp-neg 49.1%

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

      2. associate-*r/ 49.1%

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

      3. *-rgt-identity 49.1%

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

      4. +-commutative 49.1%

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

      5. exp-sum 49.2%

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

      6. rem-exp-log 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in b around 0 49.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-241} \lor \neg \left(b \leq 0.82\right):\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 13: 46.1% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-240} \lor \neg \left(b \leq 0.68\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y (* a (* b b))))))
   (if (<= b -2.05e-146)
     (- (/ x (* y a)) (* (/ x a) (/ b y)))
     (if (<= b -9e-248)
       t_1
       (if (<= b -6.2e-288)
         (/ x (/ y (- (/ 1.0 a) (/ b a))))
         (if (or (<= b 7.4e-240) (not (<= b 0.68)))
           t_1
           (/ (/ x (+ a (* a b))) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -2.05e-146) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= -9e-248) {
		tmp = t_1;
	} else if (b <= -6.2e-288) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if ((b <= 7.4e-240) || !(b <= 0.68)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * (a * (b * b)))
    if (b <= (-2.05d-146)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= (-9d-248)) then
        tmp = t_1
    else if (b <= (-6.2d-288)) then
        tmp = x / (y / ((1.0d0 / a) - (b / a)))
    else if ((b <= 7.4d-240) .or. (.not. (b <= 0.68d0))) then
        tmp = t_1
    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 t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -2.05e-146) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= -9e-248) {
		tmp = t_1;
	} else if (b <= -6.2e-288) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if ((b <= 7.4e-240) || !(b <= 0.68)) {
		tmp = t_1;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) / (y * (a * (b * b)))
	tmp = 0
	if b <= -2.05e-146:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= -9e-248:
		tmp = t_1
	elif b <= -6.2e-288:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	elif (b <= 7.4e-240) or not (b <= 0.68):
		tmp = t_1
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))))
	tmp = 0.0
	if (b <= -2.05e-146)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= -9e-248)
		tmp = t_1;
	elseif (b <= -6.2e-288)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))));
	elseif ((b <= 7.4e-240) || !(b <= 0.68))
		tmp = t_1;
	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)
	t_1 = (x * 2.0) / (y * (a * (b * b)));
	tmp = 0.0;
	if (b <= -2.05e-146)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= -9e-248)
		tmp = t_1;
	elseif (b <= -6.2e-288)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	elseif ((b <= 7.4e-240) || ~((b <= 0.68)))
		tmp = t_1;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e-146], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-248], t$95$1, If[LessEqual[b, -6.2e-288], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 7.4e-240], N[Not[LessEqual[b, 0.68]], $MachinePrecision]], t$95$1, N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.0499999999999999e-146

   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/ 89.5%

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

      2. *-commutative 89.5%

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

      3. +-commutative 89.5%

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

      4. associate--l+ 89.5%

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

      5. exp-sum 67.9%

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

      6. *-commutative 67.9%

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

      7. exp-to-pow 68.6%

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

      8. sub-neg 68.6%

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

      9. metadata-eval 68.6%

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

      10. exp-diff 58.9%

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

      11. *-commutative 58.9%

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

      12. exp-to-pow 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around 0 66.6%

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

      1. times-frac 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in b around 0 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

      5. *-commutative 52.2%

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

      6. times-frac 55.7%

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

   10. Simplified 55.7%

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

   if -2.0499999999999999e-146 < b < -8.9999999999999992e-248 or -6.19999999999999967e-288 < b < 7.4000000000000003e-240 or 0.680000000000000049 < b

   1. Initial program 99.0%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. +-commutative 88.7%

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

      4. associate--l+ 88.7%

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

      5. exp-sum 70.2%

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

      6. *-commutative 70.2%

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

      7. exp-to-pow 70.4%

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

      8. sub-neg 70.4%

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

      9. metadata-eval 70.4%

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

      10. exp-diff 58.4%

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

      11. *-commutative 58.4%

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

      12. exp-to-pow 58.4%

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

   3. Simplified 58.4%

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

   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. times-frac 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in y around 0 66.5%

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

   8. Taylor expanded in b around 0 52.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 52.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 52.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 52.2%

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

   10. Simplified 52.2%

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

   11. Taylor expanded in b around inf 61.2%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 61.2%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 61.2%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 60.3%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 60.3%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   if -8.9999999999999992e-248 < b < -6.19999999999999967e-288

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 51.6%

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

      1. exp-neg 51.6%

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

      2. associate-*r/ 51.6%

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

      3. *-rgt-identity 51.6%

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

      4. +-commutative 51.6%

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

      5. exp-sum 51.6%

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

      6. rem-exp-log 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in b around 0 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. associate-/l* 53.1%

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

   10. Simplified 53.1%

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

   11. Taylor expanded in x around 0 53.2%

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

       1. associate-/l* 57.8%

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

   13. Simplified 57.8%

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

   if 7.4000000000000003e-240 < b < 0.680000000000000049

   1. Initial program 94.0%

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

   2. Taylor expanded in t around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

   4. Simplified 74.7%

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

   5. Taylor expanded in y around 0 49.1%

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

      1. exp-neg 49.1%

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

      2. associate-*r/ 49.1%

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

      3. *-rgt-identity 49.1%

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

      4. +-commutative 49.1%

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

      5. exp-sum 49.2%

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

      6. rem-exp-log 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in b around 0 49.5%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-240} \lor \neg \left(b \leq 0.68\right):\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 14: 45.6% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -2.35 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y (* a (* b b))))))
   (if (<= b -2.35e-144)
     (- (/ x (* y a)) (* (/ x a) (/ b y)))
     (if (<= b -9e-249)
       t_1
       (if (<= b -2e-289)
         (/ x (/ y (- (/ 1.0 a) (/ b a))))
         (if (<= b 1.7e-241) t_1 (/ x (* a (+ y (* y (* b (* b 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -2.35e-144) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= -9e-249) {
		tmp = t_1;
	} else if (b <= -2e-289) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if (b <= 1.7e-241) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b * (b * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * (a * (b * b)))
    if (b <= (-2.35d-144)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= (-9d-249)) then
        tmp = t_1
    else if (b <= (-2d-289)) then
        tmp = x / (y / ((1.0d0 / a) - (b / a)))
    else if (b <= 1.7d-241) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * (b * (b * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) / (y * (a * (b * b)));
	double tmp;
	if (b <= -2.35e-144) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= -9e-249) {
		tmp = t_1;
	} else if (b <= -2e-289) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else if (b <= 1.7e-241) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b * (b * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) / (y * (a * (b * b)))
	tmp = 0
	if b <= -2.35e-144:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= -9e-249:
		tmp = t_1
	elif b <= -2e-289:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	elif b <= 1.7e-241:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * (b * (b * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * Float64(a * Float64(b * b))))
	tmp = 0.0
	if (b <= -2.35e-144)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= -9e-249)
		tmp = t_1;
	elseif (b <= -2e-289)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))));
	elseif (b <= 1.7e-241)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b * Float64(b * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) / (y * (a * (b * b)));
	tmp = 0.0;
	if (b <= -2.35e-144)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= -9e-249)
		tmp = t_1;
	elseif (b <= -2e-289)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	elseif (b <= 1.7e-241)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * (b * (b * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.35e-144], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-249], t$95$1, If[LessEqual[b, -2e-289], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-241], t$95$1, N[(x / N[(a * N[(y + N[(y * N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.3500000000000001e-144

   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/ 89.5%

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

      2. *-commutative 89.5%

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

      3. +-commutative 89.5%

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

      4. associate--l+ 89.5%

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

      5. exp-sum 67.9%

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

      6. *-commutative 67.9%

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

      7. exp-to-pow 68.6%

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

      8. sub-neg 68.6%

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

      9. metadata-eval 68.6%

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

      10. exp-diff 58.9%

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

      11. *-commutative 58.9%

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

      12. exp-to-pow 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in t around 0 66.6%

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

      1. times-frac 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in b around 0 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

      5. *-commutative 52.2%

         \[\leadsto \frac{x}{y \cdot a} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      6. times-frac 55.7%

         \[\leadsto \frac{x}{y \cdot a} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   10. Simplified 55.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}} \]

   if -2.3500000000000001e-144 < b < -8.99999999999999962e-249 or -2e-289 < b < 1.6999999999999999e-241

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.7%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.7%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 78.9%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 78.9%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 79.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 79.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 79.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 79.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 79.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 79.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 62.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 65.3%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 65.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 31.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 31.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 31.3%

         \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right)\right)} \]

   10. Simplified 31.3%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in b around inf 59.7%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 59.7%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 59.7%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 59.7%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   13. Simplified 59.7%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

   if -8.99999999999999962e-249 < b < -2e-289

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 78.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 78.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 78.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 78.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 78.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 51.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 51.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 51.6%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 51.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 51.6%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 51.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 53.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 53.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 53.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 53.1%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 53.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 53.1%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 53.1%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in x around 0 53.2%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   12. Step-by-step derivation

       1. associate-/l* 57.8%

          \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}} \]

   13. Simplified 57.8%

       \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}} \]

   if 1.6999999999999999e-241 < b

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 88.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 88.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 73.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 73.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 74.0%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 74.0%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 74.0%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 63.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 63.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 63.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 71.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 66.0%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 69.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 56.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 56.4%

         \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right)\right)} \]

   10. Simplified 56.4%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in b around inf 55.8%

       \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{0.5 \cdot \left({b}^{2} \cdot y\right)}\right)} \]
   12. Step-by-step derivation

       1. unpow2 55.8%

          \[\leadsto \frac{x}{a \cdot \left(y + 0.5 \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)\right)} \]

       2. associate-*r* 55.8%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(0.5 \cdot \left(b \cdot b\right)\right) \cdot y}\right)} \]

       3. *-commutative 55.8%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}\right)} \]

       4. *-commutative 55.8%

          \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \color{blue}{\left(\left(b \cdot b\right) \cdot 0.5\right)}\right)} \]

       5. associate-*l* 55.8%

          \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \color{blue}{\left(b \cdot \left(b \cdot 0.5\right)\right)}\right)} \]

       6. *-commutative 55.8%

          \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b \cdot \color{blue}{\left(0.5 \cdot b\right)}\right)\right)} \]

   13. Simplified 55.8%

       \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b \cdot \left(0.5 \cdot b\right)\right)}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-249}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-241}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot \left(a \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \end{array} \]

Alternative 15: 41.7% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 30:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{b \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 30.0) (/ (- x (* x b)) (* y a)) (* (/ x y) (/ 2.0 (* b (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 30.0) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / y) * (2.0 / (b * (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 <= 30.0d0) then
        tmp = (x - (x * b)) / (y * a)
    else
        tmp = (x / y) * (2.0d0 / (b * (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 <= 30.0) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / y) * (2.0 / (b * (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 30.0:
		tmp = (x - (x * b)) / (y * a)
	else:
		tmp = (x / y) * (2.0 / (b * (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 30.0)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(Float64(x / y) * Float64(2.0 / Float64(b * Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 30.0)
		tmp = (x - (x * b)) / (y * a);
	else
		tmp = (x / y) * (2.0 / (b * (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 30.0], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(2.0 / N[(b * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 30

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 79.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 79.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 51.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 51.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 51.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 51.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 51.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 51.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 52.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 47.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 47.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 47.2%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 47.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 45.1%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 45.1%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in x around 0 47.2%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   12. Step-by-step derivation

       1. *-commutative 47.2%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right) \cdot x}}{y} \]

       2. sub-neg 47.2%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} + \left(-\frac{b}{a}\right)\right)} \cdot x}{y} \]

       3. mul-1-neg 47.2%

          \[\leadsto \frac{\left(\frac{1}{a} + \color{blue}{-1 \cdot \frac{b}{a}}\right) \cdot x}{y} \]

       4. +-commutative 47.2%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)} \cdot x}{y} \]

       5. *-commutative 47.2%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)}}{y} \]

       6. +-commutative 47.2%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)}}{y} \]

       7. distribute-rgt-in 46.7%

          \[\leadsto \frac{\color{blue}{\frac{1}{a} \cdot x + \left(-1 \cdot \frac{b}{a}\right) \cdot x}}{y} \]

       8. associate-*l/ 46.7%

          \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{a}} + \left(-1 \cdot \frac{b}{a}\right) \cdot x}{y} \]

       9. *-lft-identity 46.7%

          \[\leadsto \frac{\frac{\color{blue}{x}}{a} + \left(-1 \cdot \frac{b}{a}\right) \cdot x}{y} \]

       10. mul-1-neg 46.7%

           \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b}{a}\right)} \cdot x}{y} \]

       11. cancel-sign-sub-inv 46.7%

           \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{a} \cdot x}}{y} \]

       12. associate-*l/ 47.2%

           \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b \cdot x}{a}}}{y} \]

       13. div-sub 47.8%

           \[\leadsto \frac{\color{blue}{\frac{x - b \cdot x}{a}}}{y} \]

       14. associate-/r* 48.1%

           \[\leadsto \color{blue}{\frac{x - b \cdot x}{a \cdot y}} \]

       15. *-commutative 48.1%

           \[\leadsto \frac{x - \color{blue}{x \cdot b}}{a \cdot y} \]

       16. *-commutative 48.1%

           \[\leadsto \frac{x - x \cdot b}{\color{blue}{y \cdot a}} \]

   13. Simplified 48.1%

       \[\leadsto \color{blue}{\frac{x - x \cdot b}{y \cdot a}} \]

   if 30 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.5%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.5%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 65.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 65.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 65.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 65.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 65.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 47.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 47.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 47.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 47.2%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 66.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 59.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 82.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 60.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 60.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 60.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 60.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 60.8%

         \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right)\right)} \]

   10. Simplified 60.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in b around inf 60.8%

       \[\leadsto \color{blue}{2 \cdot \frac{x}{a \cdot \left({b}^{2} \cdot y\right)}} \]
   12. Step-by-step derivation

       1. associate-*r/ 60.8%

          \[\leadsto \color{blue}{\frac{2 \cdot x}{a \cdot \left({b}^{2} \cdot y\right)}} \]

       2. unpow2 60.8%

          \[\leadsto \frac{2 \cdot x}{a \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)} \]

       3. associate-*r* 59.4%

          \[\leadsto \frac{2 \cdot x}{\color{blue}{\left(a \cdot \left(b \cdot b\right)\right) \cdot y}} \]

       4. times-frac 53.9%

          \[\leadsto \color{blue}{\frac{2}{a \cdot \left(b \cdot b\right)} \cdot \frac{x}{y}} \]

       5. associate-*r* 51.3%

          \[\leadsto \frac{2}{\color{blue}{\left(a \cdot b\right) \cdot b}} \cdot \frac{x}{y} \]

   13. Simplified 51.3%

       \[\leadsto \color{blue}{\frac{2}{\left(a \cdot b\right) \cdot b} \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 30:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{b \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 16: 42.9% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 0.95:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(b \cdot \left(y \cdot b\right)\right) \cdot \left(a \cdot 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 0.95) (/ (- x (* x b)) (* y a)) (/ x (* (* b (* y b)) (* a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 0.95) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = x / ((b * (y * b)) * (a * 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 0.95d0) then
        tmp = (x - (x * b)) / (y * a)
    else
        tmp = x / ((b * (y * b)) * (a * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 0.95) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = x / ((b * (y * b)) * (a * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 0.95:
		tmp = (x - (x * b)) / (y * a)
	else:
		tmp = x / ((b * (y * b)) * (a * 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 0.95)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(Float64(b * Float64(y * b)) * Float64(a * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 0.95)
		tmp = (x - (x * b)) / (y * a);
	else
		tmp = x / ((b * (y * b)) * (a * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 0.95], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(b * N[(y * b), $MachinePrecision]), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 0.94999999999999996

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 79.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 79.2%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 79.2%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 79.2%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 79.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 51.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 51.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 51.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 51.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 51.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 51.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 52.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 47.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 47.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 47.2%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 47.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 45.0%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 45.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in x around 0 47.2%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   12. Step-by-step derivation

       1. *-commutative 47.2%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right) \cdot x}}{y} \]

       2. sub-neg 47.2%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} + \left(-\frac{b}{a}\right)\right)} \cdot x}{y} \]

       3. mul-1-neg 47.2%

          \[\leadsto \frac{\left(\frac{1}{a} + \color{blue}{-1 \cdot \frac{b}{a}}\right) \cdot x}{y} \]

       4. +-commutative 47.2%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)} \cdot x}{y} \]

       5. *-commutative 47.2%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)}}{y} \]

       6. +-commutative 47.2%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)}}{y} \]

       7. distribute-rgt-in 46.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{a} \cdot x + \left(-1 \cdot \frac{b}{a}\right) \cdot x}}{y} \]

       8. associate-*l/ 46.6%

          \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{a}} + \left(-1 \cdot \frac{b}{a}\right) \cdot x}{y} \]

       9. *-lft-identity 46.6%

          \[\leadsto \frac{\frac{\color{blue}{x}}{a} + \left(-1 \cdot \frac{b}{a}\right) \cdot x}{y} \]

       10. mul-1-neg 46.6%

           \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b}{a}\right)} \cdot x}{y} \]

       11. cancel-sign-sub-inv 46.6%

           \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{a} \cdot x}}{y} \]

       12. associate-*l/ 47.2%

           \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b \cdot x}{a}}}{y} \]

       13. div-sub 47.7%

           \[\leadsto \frac{\color{blue}{\frac{x - b \cdot x}{a}}}{y} \]

       14. associate-/r* 47.5%

           \[\leadsto \color{blue}{\frac{x - b \cdot x}{a \cdot y}} \]

       15. *-commutative 47.5%

           \[\leadsto \frac{x - \color{blue}{x \cdot b}}{a \cdot y} \]

       16. *-commutative 47.5%

           \[\leadsto \frac{x - x \cdot b}{\color{blue}{y \cdot a}} \]

   13. Simplified 47.5%

       \[\leadsto \color{blue}{\frac{x - x \cdot b}{y \cdot a}} \]

   if 0.94999999999999996 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.8%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.8%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 66.2%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 66.2%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 66.2%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 66.2%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 66.2%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 48.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 48.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 48.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 48.6%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 67.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 60.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 82.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 61.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right)\right)} \]

   10. Simplified 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in b around inf 61.8%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)}} \]
   12. Step-by-step derivation

       1. *-commutative 61.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot \left({b}^{2} \cdot y\right)\right) \cdot 0.5}} \]

       2. *-commutative 61.8%

          \[\leadsto \frac{x}{\color{blue}{\left(\left({b}^{2} \cdot y\right) \cdot a\right)} \cdot 0.5} \]

       3. associate-*l* 61.8%

          \[\leadsto \frac{x}{\color{blue}{\left({b}^{2} \cdot y\right) \cdot \left(a \cdot 0.5\right)}} \]

       4. unpow2 61.8%

          \[\leadsto \frac{x}{\left(\color{blue}{\left(b \cdot b\right)} \cdot y\right) \cdot \left(a \cdot 0.5\right)} \]

       5. associate-*l* 56.6%

          \[\leadsto \frac{x}{\color{blue}{\left(b \cdot \left(b \cdot y\right)\right)} \cdot \left(a \cdot 0.5\right)} \]

       6. *-commutative 56.6%

          \[\leadsto \frac{x}{\left(b \cdot \color{blue}{\left(y \cdot b\right)}\right) \cdot \left(a \cdot 0.5\right)} \]

   13. Simplified 56.6%

       \[\leadsto \frac{x}{\color{blue}{\left(b \cdot \left(y \cdot b\right)\right) \cdot \left(a \cdot 0.5\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 0.95:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(b \cdot \left(y \cdot b\right)\right) \cdot \left(a \cdot 0.5\right)}\\ \end{array} \]

Alternative 17: 43.7% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 0.96:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(b \cdot \left(y \cdot b\right)\right) \cdot \left(a \cdot 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 0.96)
   (/ x (/ y (- (/ 1.0 a) (/ b a))))
   (/ x (* (* b (* y b)) (* a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 0.96) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else {
		tmp = x / ((b * (y * b)) * (a * 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 0.96d0) then
        tmp = x / (y / ((1.0d0 / a) - (b / a)))
    else
        tmp = x / ((b * (y * b)) * (a * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 0.96) {
		tmp = x / (y / ((1.0 / a) - (b / a)));
	} else {
		tmp = x / ((b * (y * b)) * (a * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 0.96:
		tmp = x / (y / ((1.0 / a) - (b / a)))
	else:
		tmp = x / ((b * (y * b)) * (a * 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 0.96)
		tmp = Float64(x / Float64(y / Float64(Float64(1.0 / a) - Float64(b / a))));
	else
		tmp = Float64(x / Float64(Float64(b * Float64(y * b)) * Float64(a * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 0.96)
		tmp = x / (y / ((1.0 / a) - (b / a)));
	else
		tmp = x / ((b * (y * b)) * (a * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 0.96], N[(x / N[(y / N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(b * N[(y * b), $MachinePrecision]), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 0.95999999999999996

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 79.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 79.2%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 79.2%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 79.2%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 79.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 51.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 51.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 51.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 51.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 51.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 51.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 52.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 47.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 47.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 47.2%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 47.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 45.0%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 45.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in x around 0 47.2%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   12. Step-by-step derivation

       1. associate-/l* 48.6%

          \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}} \]

   13. Simplified 48.6%

       \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}} \]

   if 0.95999999999999996 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.8%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.8%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 66.2%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 66.2%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 66.2%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 66.2%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 66.2%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 48.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 48.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 48.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 48.6%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 67.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 60.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 82.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 61.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 61.8%

         \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right)\right)} \]

   10. Simplified 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   11. Taylor expanded in b around inf 61.8%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)}} \]
   12. Step-by-step derivation

       1. *-commutative 61.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot \left({b}^{2} \cdot y\right)\right) \cdot 0.5}} \]

       2. *-commutative 61.8%

          \[\leadsto \frac{x}{\color{blue}{\left(\left({b}^{2} \cdot y\right) \cdot a\right)} \cdot 0.5} \]

       3. associate-*l* 61.8%

          \[\leadsto \frac{x}{\color{blue}{\left({b}^{2} \cdot y\right) \cdot \left(a \cdot 0.5\right)}} \]

       4. unpow2 61.8%

          \[\leadsto \frac{x}{\left(\color{blue}{\left(b \cdot b\right)} \cdot y\right) \cdot \left(a \cdot 0.5\right)} \]

       5. associate-*l* 56.6%

          \[\leadsto \frac{x}{\color{blue}{\left(b \cdot \left(b \cdot y\right)\right)} \cdot \left(a \cdot 0.5\right)} \]

       6. *-commutative 56.6%

          \[\leadsto \frac{x}{\left(b \cdot \color{blue}{\left(y \cdot b\right)}\right) \cdot \left(a \cdot 0.5\right)} \]

   13. Simplified 56.6%

       \[\leadsto \frac{x}{\color{blue}{\left(b \cdot \left(y \cdot b\right)\right) \cdot \left(a \cdot 0.5\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 0.96:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{1}{a} - \frac{b}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(b \cdot \left(y \cdot b\right)\right) \cdot \left(a \cdot 0.5\right)}\\ \end{array} \]

Alternative 18: 38.3% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{b \cdot \left(-\frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.1e-50) (/ (* b (- (/ x a))) y) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e-50) {
		tmp = (b * -(x / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.1d-50)) then
        tmp = (b * -(x / a)) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e-50) {
		tmp = (b * -(x / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.1e-50:
		tmp = (b * -(x / a)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.1e-50)
		tmp = Float64(Float64(b * Float64(-Float64(x / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.1e-50)
		tmp = (b * -(x / a)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.1e-50], N[(N[(b * (-N[(x / a), $MachinePrecision])), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1000000000000002e-50

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 84.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 84.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 84.0%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 84.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 84.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 69.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 69.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 69.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 69.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 69.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 70.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 70.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 56.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 56.6%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 56.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 53.5%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 53.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in b around inf 46.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-*r/ 46.0%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. associate-/r* 53.6%

          \[\leadsto \color{blue}{\frac{\frac{-1 \cdot \left(b \cdot x\right)}{a}}{y}} \]

       3. mul-1-neg 53.6%

          \[\leadsto \frac{\frac{\color{blue}{-b \cdot x}}{a}}{y} \]

       4. *-commutative 53.6%

          \[\leadsto \frac{\frac{-\color{blue}{x \cdot b}}{a}}{y} \]

       5. distribute-rgt-neg-in 53.6%

          \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(-b\right)}}{a}}{y} \]

       6. neg-mul-1 53.6%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\left(-1 \cdot b\right)}}{a}}{y} \]

       7. associate-*l/ 52.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(-1 \cdot b\right)}}{y} \]

       8. neg-mul-1 52.1%

          \[\leadsto \frac{\frac{x}{a} \cdot \color{blue}{\left(-b\right)}}{y} \]

   13. Simplified 52.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot \left(-b\right)}{y}} \]

   if -3.1000000000000002e-50 < b

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 88.3%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 88.3%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 69.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 69.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 69.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 68.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 60.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 40.7%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 42.7%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 42.7%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 42.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{b \cdot \left(-\frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 19: 39.1% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-50}:\\ \;\;\;\;\frac{-\frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.7e-50) (/ (- (/ (* x b) a)) y) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e-50) {
		tmp = -((x * b) / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.7d-50)) then
        tmp = -((x * b) / a) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e-50) {
		tmp = -((x * b) / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.7e-50:
		tmp = -((x * b) / a) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.7e-50)
		tmp = Float64(Float64(-Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.7e-50)
		tmp = -((x * b) / a) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.7e-50], N[((-N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]) / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.70000000000000007e-50

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 84.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 84.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 84.0%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 84.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 84.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 69.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 69.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 69.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 69.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 69.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 70.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 70.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 56.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 56.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 56.6%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 56.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 53.5%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 53.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in b around inf 53.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]

   if -1.70000000000000007e-50 < b

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 88.3%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 88.3%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 69.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 69.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 69.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 68.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 60.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 40.7%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. distribute-lft-out 42.7%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

      2. *-commutative 42.7%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   10. Simplified 42.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-50}:\\ \;\;\;\;\frac{-\frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 20: 39.4% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-292}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e-292) (/ (- x (* x b)) (* 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 <= -4e-292) {
		tmp = (x - (x * b)) / (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 <= (-4d-292)) then
        tmp = (x - (x * b)) / (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 <= -4e-292) {
		tmp = (x - (x * b)) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e-292:
		tmp = (x - (x * b)) / (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 <= -4e-292)
		tmp = Float64(Float64(x - Float64(x * b)) / 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 <= -4e-292)
		tmp = (x - (x * b)) / (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, -4e-292], N[(N[(x - N[(x * b), $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 < -4.0000000000000002e-292

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 80.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 80.3%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 80.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 80.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 55.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 55.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 55.3%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 55.3%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 55.3%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 55.3%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 56.0%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 49.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 49.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 49.0%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 49.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 47.4%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 47.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in x around 0 48.2%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   12. Step-by-step derivation

       1. *-commutative 48.2%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right) \cdot x}}{y} \]

       2. sub-neg 48.2%

          \[\leadsto \frac{\color{blue}{\left(\frac{1}{a} + \left(-\frac{b}{a}\right)\right)} \cdot x}{y} \]

       3. mul-1-neg 48.2%

          \[\leadsto \frac{\left(\frac{1}{a} + \color{blue}{-1 \cdot \frac{b}{a}}\right) \cdot x}{y} \]

       4. +-commutative 48.2%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)} \cdot x}{y} \]

       5. *-commutative 48.2%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)}}{y} \]

       6. +-commutative 48.2%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)}}{y} \]

       7. distribute-rgt-in 48.2%

          \[\leadsto \frac{\color{blue}{\frac{1}{a} \cdot x + \left(-1 \cdot \frac{b}{a}\right) \cdot x}}{y} \]

       8. associate-*l/ 48.2%

          \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{a}} + \left(-1 \cdot \frac{b}{a}\right) \cdot x}{y} \]

       9. *-lft-identity 48.2%

          \[\leadsto \frac{\frac{\color{blue}{x}}{a} + \left(-1 \cdot \frac{b}{a}\right) \cdot x}{y} \]

       10. mul-1-neg 48.2%

           \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b}{a}\right)} \cdot x}{y} \]

       11. cancel-sign-sub-inv 48.2%

           \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{a} \cdot x}}{y} \]

       12. associate-*l/ 49.0%

           \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b \cdot x}{a}}}{y} \]

       13. div-sub 49.0%

           \[\leadsto \frac{\color{blue}{\frac{x - b \cdot x}{a}}}{y} \]

       14. associate-/r* 49.7%

           \[\leadsto \color{blue}{\frac{x - b \cdot x}{a \cdot y}} \]

       15. *-commutative 49.7%

           \[\leadsto \frac{x - \color{blue}{x \cdot b}}{a \cdot y} \]

       16. *-commutative 49.7%

           \[\leadsto \frac{x - x \cdot b}{\color{blue}{y \cdot a}} \]

   13. Simplified 49.7%

       \[\leadsto \color{blue}{\frac{x - x \cdot b}{y \cdot a}} \]

   if -4.0000000000000002e-292 < b

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 84.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 84.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 84.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 84.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 84.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 64.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 64.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 64.6%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 64.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 64.6%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 64.6%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 65.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 41.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-292}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 21: 34.5% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.45:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.45) (/ (- (* x b)) (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.45) {
		tmp = -(x * b) / (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 <= (-0.45d0)) then
        tmp = -(x * b) / (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 <= -0.45) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.45:
		tmp = -(x * b) / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.45)
		tmp = Float64(Float64(-Float64(x * b)) / 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 <= -0.45)
		tmp = -(x * b) / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.45], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.450000000000000011

   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 88.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 88.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 88.1%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 88.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 88.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 74.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 74.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 74.4%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 74.4%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 74.4%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 74.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 74.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 57.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 57.7%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 57.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 53.9%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

   10. Simplified 53.9%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b}{\frac{a}{x}}}}{y} \]

   11. Taylor expanded in b around inf 55.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-*r/ 55.6%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. mul-1-neg 55.6%

          \[\leadsto \frac{\color{blue}{-b \cdot x}}{a \cdot y} \]

       3. *-commutative 55.6%

          \[\leadsto \frac{-\color{blue}{x \cdot b}}{a \cdot y} \]

       4. *-commutative 55.6%

          \[\leadsto \frac{-x \cdot b}{\color{blue}{y \cdot a}} \]

   13. Simplified 55.6%

       \[\leadsto \color{blue}{\frac{-x \cdot b}{y \cdot a}} \]

   if -0.450000000000000011 < b

   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. Taylor expanded in t around 0 81.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 81.2%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 81.2%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 81.2%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 81.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 56.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 56.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 56.9%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 56.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 56.9%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 56.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 57.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 57.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 35.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.45:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 22: 31.2% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 3.3 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 3.3e-118) (/ (/ x a) y) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.3e-118) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 3.3d-118) then
        tmp = (x / a) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.3e-118) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 3.3e-118:
		tmp = (x / a) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 3.3e-118)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 3.3e-118)
		tmp = (x / a) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.3e-118], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.3e-118

   1. Initial program 98.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 88.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 88.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 88.5%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 88.5%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 88.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 66.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 66.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 66.2%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 66.2%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 66.2%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 66.3%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 67.2%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 39.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 3.3e-118 < t

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.9%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.9%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 66.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 66.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 67.0%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 67.0%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 67.0%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 62.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 62.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 62.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   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. times-frac 50.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 50.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 25.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 25.8%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 25.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   11. Step-by-step derivation

       1. div-inv 25.8%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

       2. add-exp-log 12.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{e^{\log \left(y \cdot a\right)}}} \]

       3. rec-exp 12.8%

          \[\leadsto x \cdot \color{blue}{e^{-\log \left(y \cdot a\right)}} \]

       4. log-prod 12.7%

          \[\leadsto x \cdot e^{-\color{blue}{\left(\log y + \log a\right)}} \]

       5. pow1 12.7%

          \[\leadsto x \cdot e^{-\left(\log y + \log \color{blue}{\left({a}^{1}\right)}\right)} \]

       6. metadata-eval 12.7%

          \[\leadsto x \cdot e^{-\left(\log y + \log \left({a}^{\color{blue}{\left(--1\right)}}\right)\right)} \]

       7. pow-flip 12.7%

          \[\leadsto x \cdot e^{-\left(\log y + \log \color{blue}{\left(\frac{1}{{a}^{-1}}\right)}\right)} \]

       8. inv-pow 12.7%

          \[\leadsto x \cdot e^{-\left(\log y + \log \left(\frac{1}{\color{blue}{\frac{1}{a}}}\right)\right)} \]

       9. log-prod 12.8%

          \[\leadsto x \cdot e^{-\color{blue}{\log \left(y \cdot \frac{1}{\frac{1}{a}}\right)}} \]

       10. div-inv 12.8%

           \[\leadsto x \cdot e^{-\log \color{blue}{\left(\frac{y}{\frac{1}{a}}\right)}} \]

       11. rec-exp 12.8%

           \[\leadsto x \cdot \color{blue}{\frac{1}{e^{\log \left(\frac{y}{\frac{1}{a}}\right)}}} \]

       12. add-exp-log 25.8%

           \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{y}{\frac{1}{a}}}} \]

       13. div-inv 25.8%

           \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{1}{a}}}} \]

       14. associate-/r/ 32.9%

           \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   12. Applied egg-rr 32.9%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.3 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]

Alternative 23: 30.5% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 9.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 9.8e-82) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 9.8e-82) {
		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 (z <= 9.8d-82) 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 (z <= 9.8e-82) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 9.8e-82:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 9.8e-82)
		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 (z <= 9.8e-82)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 9.8e-82], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.8000000000000006e-82

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 85.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 85.6%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 85.6%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 68.2%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 68.2%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 68.9%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 68.9%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 68.9%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 64.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 64.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 64.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 64.1%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 73.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 66.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Taylor expanded in y around 0 62.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 36.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 36.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if 9.8000000000000006e-82 < z

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 82.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   3. Step-by-step derivation

      1. +-commutative 82.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 82.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 82.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   4. Simplified 82.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   5. Taylor expanded in y around 0 61.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-\left(b + \log a\right)}}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 61.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 61.3%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 61.3%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 61.3%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 61.3%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 62.0%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   8. Taylor expanded in b around 0 36.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 24: 30.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 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. *-commutative 89.1%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. +-commutative 89.1%

      \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

   4. associate--l+ 89.1%

      \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

   5. exp-sum 72.7%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 72.7%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 73.4%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 73.4%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 73.4%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 65.2%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 65.2%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 65.2%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 65.2%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

4. Taylor expanded in t around 0 68.8%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
5. Step-by-step derivation

   1. times-frac 66.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

6. Simplified 66.1%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Taylor expanded in y around 0 61.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

8. Taylor expanded in b around 0 35.0%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
9. Step-by-step derivation

   1. *-commutative 35.0%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

10. Simplified 35.0%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

11. Final simplification 35.0%

    \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 71.3% 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 2023290 
(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))