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

Percentage Accurate: 98.3% → 98.3%

Time: 20.6s

Alternatives: 21

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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

2. Final simplification 97.8%

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

Alternative 2: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+96} \lor \neg \left(y \leq 8.5 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+96) (not (<= y 8.5e+136)))
   (/ (* 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 <= -5e+96) || !(y <= 8.5e+136)) {
		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 <= (-5d+96)) .or. (.not. (y <= 8.5d+136))) 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 <= -5e+96) || !(y <= 8.5e+136)) {
		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 <= -5e+96) or not (y <= 8.5e+136):
		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 <= -5e+96) || !(y <= 8.5e+136))
		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 <= -5e+96) || ~((y <= 8.5e+136)))
		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, -5e+96], N[Not[LessEqual[y, 8.5e+136]], $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 < -5.0000000000000004e96 or 8.49999999999999966e136 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 97.7%

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

   if -5.0000000000000004e96 < y < 8.49999999999999966e136

   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. Taylor expanded in y around 0 91.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+96} \lor \neg \left(y \leq 8.5 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 75.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{t}}{y \cdot a} \cdot \frac{x}{e^{b}}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2900:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a t) (* y a)) (/ x (exp b))))
        (t_2 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -5.8e+96)
     t_2
     (if (<= y -9e+33)
       t_1
       (if (<= y -2900.0)
         t_2
         (if (<= y -2.45e-142)
           (/ (* x (pow a (+ t -1.0))) y)
           (if (<= y 6.5e+121) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, t) / (y * a)) * (x / exp(b));
	double t_2 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.8e+96) {
		tmp = t_2;
	} else if (y <= -9e+33) {
		tmp = t_1;
	} else if (y <= -2900.0) {
		tmp = t_2;
	} else if (y <= -2.45e-142) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 6.5e+121) {
		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 = ((a ** t) / (y * a)) * (x / exp(b))
    t_2 = ((x * (z ** y)) / a) / y
    if (y <= (-5.8d+96)) then
        tmp = t_2
    else if (y <= (-9d+33)) then
        tmp = t_1
    else if (y <= (-2900.0d0)) then
        tmp = t_2
    else if (y <= (-2.45d-142)) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 6.5d+121) 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 = (Math.pow(a, t) / (y * a)) * (x / Math.exp(b));
	double t_2 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -5.8e+96) {
		tmp = t_2;
	} else if (y <= -9e+33) {
		tmp = t_1;
	} else if (y <= -2900.0) {
		tmp = t_2;
	} else if (y <= -2.45e-142) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 6.5e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, t) / (y * a)) * (x / math.exp(b))
	t_2 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -5.8e+96:
		tmp = t_2
	elif y <= -9e+33:
		tmp = t_1
	elif y <= -2900.0:
		tmp = t_2
	elif y <= -2.45e-142:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 6.5e+121:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ t) / Float64(y * a)) * Float64(x / exp(b)))
	t_2 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -5.8e+96)
		tmp = t_2;
	elseif (y <= -9e+33)
		tmp = t_1;
	elseif (y <= -2900.0)
		tmp = t_2;
	elseif (y <= -2.45e-142)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 6.5e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ t) / (y * a)) * (x / exp(b));
	t_2 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -5.8e+96)
		tmp = t_2;
	elseif (y <= -9e+33)
		tmp = t_1;
	elseif (y <= -2900.0)
		tmp = t_2;
	elseif (y <= -2.45e-142)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 6.5e+121)
		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[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -5.8e+96], t$95$2, If[LessEqual[y, -9e+33], t$95$1, If[LessEqual[y, -2900.0], t$95$2, If[LessEqual[y, -2.45e-142], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.5e+121], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999955e96 or -9.0000000000000001e33 < y < -2900 or 6.50000000000000019e121 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

      3. +-commutative 87.2%

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

      4. associate--l+ 87.2%

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

      5. exp-sum 67.0%

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

      6. *-commutative 67.0%

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

      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 53.2%

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

      11. *-commutative 53.2%

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

      12. exp-to-pow 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in b around 0 66.0%

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

   5. Taylor expanded in t around 0 90.6%

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

   if -5.79999999999999955e96 < y < -9.0000000000000001e33 or -2.4500000000000002e-142 < y < 6.50000000000000019e121

   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. Step-by-step derivation

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

      3. +-commutative 89.8%

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

      4. associate--l+ 89.8%

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

      5. exp-sum 74.1%

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

      6. *-commutative 74.1%

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

      7. exp-to-pow 74.9%

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

      8. sub-neg 74.9%

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

      9. metadata-eval 74.9%

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

      10. exp-diff 69.4%

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

      11. *-commutative 69.4%

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

      12. exp-to-pow 69.4%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in y around 0 80.4%

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

      1. times-frac 81.1%

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

      2. sub-neg 81.1%

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

      3. metadata-eval 81.1%

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

   6. Simplified 81.1%

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

      1. expm1-log1p-u 54.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 49.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 50.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 50.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 53.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 80.4%

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

      3. *-commutative 80.4%

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

      4. times-frac 81.2%

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

      5. associate-/l/ 79.7%

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

      6. *-commutative 79.7%

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

   10. Simplified 79.7%

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

   if -2900 < y < -2.4500000000000002e-142

   1. Initial program 95.4%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

      3. +-commutative 92.5%

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

      4. associate--l+ 92.5%

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

      5. exp-sum 81.2%

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

      6. *-commutative 81.2%

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

      7. exp-to-pow 82.9%

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

      8. sub-neg 82.9%

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

      9. metadata-eval 82.9%

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

      10. exp-diff 80.0%

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

      11. *-commutative 80.0%

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

      12. exp-to-pow 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in y around 0 85.7%

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

      1. times-frac 82.9%

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

      2. sub-neg 82.9%

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

      3. metadata-eval 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in b around 0 80.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+33}:\\ \;\;\;\;\frac{{a}^{t}}{y \cdot a} \cdot \frac{x}{e^{b}}\\ \mathbf{elif}\;y \leq -2900:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{{a}^{t}}{y \cdot a} \cdot \frac{x}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 4: 78.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t + -1\right)}\\ t_2 := \frac{x}{e^{b}}\\ t_3 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{{a}^{t}}{y \cdot a} \cdot t_2\\ \mathbf{elif}\;y \leq -3100:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;t_2 \cdot \frac{t_1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (+ t -1.0)))
        (t_2 (/ x (exp b)))
        (t_3 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -4.8e+96)
     t_3
     (if (<= y -2.1e+34)
       (* (/ (pow a t) (* y a)) t_2)
       (if (<= y -3100.0)
         t_3
         (if (<= y -2.8e-50)
           (/ (* x t_1) y)
           (if (<= y 6.5e+121) (* t_2 (/ t_1 y)) 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 = x / exp(b);
	double t_3 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4.8e+96) {
		tmp = t_3;
	} else if (y <= -2.1e+34) {
		tmp = (pow(a, t) / (y * a)) * t_2;
	} else if (y <= -3100.0) {
		tmp = t_3;
	} else if (y <= -2.8e-50) {
		tmp = (x * t_1) / y;
	} else if (y <= 6.5e+121) {
		tmp = t_2 * (t_1 / y);
	} 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 = x / exp(b)
    t_3 = ((x * (z ** y)) / a) / y
    if (y <= (-4.8d+96)) then
        tmp = t_3
    else if (y <= (-2.1d+34)) then
        tmp = ((a ** t) / (y * a)) * t_2
    else if (y <= (-3100.0d0)) then
        tmp = t_3
    else if (y <= (-2.8d-50)) then
        tmp = (x * t_1) / y
    else if (y <= 6.5d+121) then
        tmp = t_2 * (t_1 / y)
    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 = x / Math.exp(b);
	double t_3 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4.8e+96) {
		tmp = t_3;
	} else if (y <= -2.1e+34) {
		tmp = (Math.pow(a, t) / (y * a)) * t_2;
	} else if (y <= -3100.0) {
		tmp = t_3;
	} else if (y <= -2.8e-50) {
		tmp = (x * t_1) / y;
	} else if (y <= 6.5e+121) {
		tmp = t_2 * (t_1 / y);
	} 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 = x / math.exp(b)
	t_3 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -4.8e+96:
		tmp = t_3
	elif y <= -2.1e+34:
		tmp = (math.pow(a, t) / (y * a)) * t_2
	elif y <= -3100.0:
		tmp = t_3
	elif y <= -2.8e-50:
		tmp = (x * t_1) / y
	elif y <= 6.5e+121:
		tmp = t_2 * (t_1 / y)
	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(x / exp(b))
	t_3 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -4.8e+96)
		tmp = t_3;
	elseif (y <= -2.1e+34)
		tmp = Float64(Float64((a ^ t) / Float64(y * a)) * t_2);
	elseif (y <= -3100.0)
		tmp = t_3;
	elseif (y <= -2.8e-50)
		tmp = Float64(Float64(x * t_1) / y);
	elseif (y <= 6.5e+121)
		tmp = Float64(t_2 * Float64(t_1 / y));
	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 = x / exp(b);
	t_3 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -4.8e+96)
		tmp = t_3;
	elseif (y <= -2.1e+34)
		tmp = ((a ^ t) / (y * a)) * t_2;
	elseif (y <= -3100.0)
		tmp = t_3;
	elseif (y <= -2.8e-50)
		tmp = (x * t_1) / y;
	elseif (y <= 6.5e+121)
		tmp = t_2 * (t_1 / y);
	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[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.8e+96], t$95$3, If[LessEqual[y, -2.1e+34], N[(N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[y, -3100.0], t$95$3, If[LessEqual[y, -2.8e-50], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.5e+121], N[(t$95$2 * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.79999999999999986e96 or -2.10000000000000017e34 < y < -3100 or 6.50000000000000019e121 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

      3. +-commutative 87.2%

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

      4. associate--l+ 87.2%

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

      5. exp-sum 67.0%

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

      6. *-commutative 67.0%

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

      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 53.2%

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

      11. *-commutative 53.2%

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

      12. exp-to-pow 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in b around 0 66.0%

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

   5. Taylor expanded in t around 0 90.6%

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

   if -4.79999999999999986e96 < y < -2.10000000000000017e34

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. exp-sum 62.5%

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

      6. *-commutative 62.5%

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

      7. exp-to-pow 62.5%

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

      8. sub-neg 62.5%

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

      9. metadata-eval 62.5%

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

      10. exp-diff 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 y around 0 81.6%

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

      1. times-frac 81.6%

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

      2. sub-neg 81.6%

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

      3. metadata-eval 81.6%

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

   6. Simplified 81.6%

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

      1. expm1-log1p-u 37.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 37.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 37.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 37.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 81.6%

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

      3. *-commutative 81.6%

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

      4. times-frac 81.6%

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

      5. associate-/l/ 81.6%

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

      6. *-commutative 81.6%

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

   10. Simplified 81.6%

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

   if -3100 < y < -2.7999999999999998e-50

   1. Initial program 91.7%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

      3. +-commutative 91.7%

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

      4. associate--l+ 91.7%

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

      5. exp-sum 68.6%

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

      6. *-commutative 68.6%

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

      7. exp-to-pow 69.5%

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

      8. sub-neg 69.5%

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

      9. metadata-eval 69.5%

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

      10. exp-diff 61.8%

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

      11. *-commutative 61.8%

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

      12. exp-to-pow 61.8%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in y around 0 69.2%

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

      1. times-frac 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in b around 0 77.1%

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

   if -2.7999999999999998e-50 < y < 6.50000000000000019e121

   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/ 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 77.9%

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

      6. *-commutative 77.9%

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

      7. exp-to-pow 79.0%

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

      8. sub-neg 79.0%

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

      9. metadata-eval 79.0%

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

      10. exp-diff 75.2%

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

      11. *-commutative 75.2%

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

      12. exp-to-pow 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around 0 82.7%

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

      1. times-frac 82.7%

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

      2. sub-neg 82.7%

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

      3. metadata-eval 82.7%

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

   6. Simplified 82.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{{a}^{t}}{y \cdot a} \cdot \frac{x}{e^{b}}\\ \mathbf{elif}\;y \leq -3100:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{e^{b}} \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 5: 80.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t + -1\right)}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{{a}^{t}}{y \cdot a} \cdot \frac{x}{e^{b}}\\ \mathbf{elif}\;y \leq -3200000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x \cdot \frac{t_1}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (+ t -1.0))) (t_2 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -4.8e+96)
     t_2
     (if (<= y -7.5e+33)
       (* (/ (pow a t) (* y a)) (/ x (exp b)))
       (if (<= y -3200000.0)
         t_2
         (if (<= y -1.3e-48)
           (/ (* x t_1) y)
           (if (<= y 6.5e+121) (/ (* x (/ t_1 (exp b))) 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 * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4.8e+96) {
		tmp = t_2;
	} else if (y <= -7.5e+33) {
		tmp = (pow(a, t) / (y * a)) * (x / exp(b));
	} else if (y <= -3200000.0) {
		tmp = t_2;
	} else if (y <= -1.3e-48) {
		tmp = (x * t_1) / y;
	} else if (y <= 6.5e+121) {
		tmp = (x * (t_1 / exp(b))) / 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 * (z ** y)) / a) / y
    if (y <= (-4.8d+96)) then
        tmp = t_2
    else if (y <= (-7.5d+33)) then
        tmp = ((a ** t) / (y * a)) * (x / exp(b))
    else if (y <= (-3200000.0d0)) then
        tmp = t_2
    else if (y <= (-1.3d-48)) then
        tmp = (x * t_1) / y
    else if (y <= 6.5d+121) then
        tmp = (x * (t_1 / exp(b))) / 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 * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -4.8e+96) {
		tmp = t_2;
	} else if (y <= -7.5e+33) {
		tmp = (Math.pow(a, t) / (y * a)) * (x / Math.exp(b));
	} else if (y <= -3200000.0) {
		tmp = t_2;
	} else if (y <= -1.3e-48) {
		tmp = (x * t_1) / y;
	} else if (y <= 6.5e+121) {
		tmp = (x * (t_1 / Math.exp(b))) / 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 * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -4.8e+96:
		tmp = t_2
	elif y <= -7.5e+33:
		tmp = (math.pow(a, t) / (y * a)) * (x / math.exp(b))
	elif y <= -3200000.0:
		tmp = t_2
	elif y <= -1.3e-48:
		tmp = (x * t_1) / y
	elif y <= 6.5e+121:
		tmp = (x * (t_1 / math.exp(b))) / 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(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -4.8e+96)
		tmp = t_2;
	elseif (y <= -7.5e+33)
		tmp = Float64(Float64((a ^ t) / Float64(y * a)) * Float64(x / exp(b)));
	elseif (y <= -3200000.0)
		tmp = t_2;
	elseif (y <= -1.3e-48)
		tmp = Float64(Float64(x * t_1) / y);
	elseif (y <= 6.5e+121)
		tmp = Float64(Float64(x * Float64(t_1 / exp(b))) / 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 * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -4.8e+96)
		tmp = t_2;
	elseif (y <= -7.5e+33)
		tmp = ((a ^ t) / (y * a)) * (x / exp(b));
	elseif (y <= -3200000.0)
		tmp = t_2;
	elseif (y <= -1.3e-48)
		tmp = (x * t_1) / y;
	elseif (y <= 6.5e+121)
		tmp = (x * (t_1 / exp(b))) / 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[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.8e+96], t$95$2, If[LessEqual[y, -7.5e+33], N[(N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3200000.0], t$95$2, If[LessEqual[y, -1.3e-48], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.5e+121], N[(N[(x * N[(t$95$1 / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.79999999999999986e96 or -7.50000000000000046e33 < y < -3.2e6 or 6.50000000000000019e121 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

      3. +-commutative 87.2%

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

      4. associate--l+ 87.2%

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

      5. exp-sum 67.0%

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

      6. *-commutative 67.0%

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

      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 53.2%

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

      11. *-commutative 53.2%

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

      12. exp-to-pow 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in b around 0 66.0%

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

   5. Taylor expanded in t around 0 90.6%

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

   if -4.79999999999999986e96 < y < -7.50000000000000046e33

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. exp-sum 62.5%

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

      6. *-commutative 62.5%

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

      7. exp-to-pow 62.5%

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

      8. sub-neg 62.5%

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

      9. metadata-eval 62.5%

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

      10. exp-diff 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 y around 0 81.6%

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

      1. times-frac 81.6%

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

      2. sub-neg 81.6%

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

      3. metadata-eval 81.6%

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

   6. Simplified 81.6%

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

      1. expm1-log1p-u 37.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 37.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 37.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 37.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 37.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 81.6%

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

      3. *-commutative 81.6%

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

      4. times-frac 81.6%

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

      5. associate-/l/ 81.6%

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

      6. *-commutative 81.6%

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

   10. Simplified 81.6%

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

   if -3.2e6 < y < -1.29999999999999994e-48

   1. Initial program 91.7%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

      3. +-commutative 91.7%

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

      4. associate--l+ 91.7%

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

      5. exp-sum 68.6%

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

      6. *-commutative 68.6%

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

      7. exp-to-pow 69.5%

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

      8. sub-neg 69.5%

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

      9. metadata-eval 69.5%

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

      10. exp-diff 61.8%

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

      11. *-commutative 61.8%

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

      12. exp-to-pow 61.8%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in y around 0 69.2%

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

      1. times-frac 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in b around 0 77.1%

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

   if -1.29999999999999994e-48 < y < 6.50000000000000019e121

   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. Taylor expanded in y around 0 93.7%

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

      1. *-commutative 93.7%

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

      2. exp-diff 85.5%

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

      3. sub-neg 85.5%

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

      4. metadata-eval 85.5%

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

      5. *-commutative 85.5%

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

      6. exp-to-pow 86.5%

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

   4. Simplified 86.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{{a}^{t}}{y \cdot a} \cdot \frac{x}{e^{b}}\\ \mathbf{elif}\;y \leq -3200000:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 6: 79.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -4 \cdot 10^{+124}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+37}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -4e+124)
   (/ (* x (pow a t)) (* y a))
   (if (<= (+ t -1.0) 4e+37)
     (* (/ (pow z y) a) (/ x (* y (exp b))))
     (/ (* x (pow a (+ t -1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -4e+124) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 4e+37) {
		tmp = (pow(z, y) / a) * (x / (y * exp(b)));
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-4d+124)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t + (-1.0d0)) <= 4d+37) then
        tmp = ((z ** y) / a) * (x / (y * exp(b)))
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -4e+124) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 4e+37) {
		tmp = (Math.pow(z, y) / a) * (x / (y * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -4e+124:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t + -1.0) <= 4e+37:
		tmp = (math.pow(z, y) / a) * (x / (y * math.exp(b)))
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -4e+124)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t + -1.0) <= 4e+37)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -4e+124)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t + -1.0) <= 4e+37)
		tmp = ((z ^ y) / a) * (x / (y * exp(b)));
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -4e+124], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+37], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -3.99999999999999979e124

   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/ 92.5%

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

      2. *-commutative 92.5%

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

      3. +-commutative 92.5%

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

      4. associate--l+ 92.5%

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

      5. exp-sum 57.5%

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

      6. *-commutative 57.5%

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

      7. exp-to-pow 57.5%

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

      8. sub-neg 57.5%

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

      9. metadata-eval 57.5%

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

      10. exp-diff 55.0%

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

      11. *-commutative 55.0%

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

      12. exp-to-pow 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in y around 0 65.0%

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

      1. times-frac 65.0%

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

      2. sub-neg 65.0%

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

      3. metadata-eval 65.0%

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

   6. Simplified 65.0%

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

      1. expm1-log1p-u 40.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 40.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 40.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 40.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 40.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 40.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 40.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 40.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 40.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 40.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 65.0%

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

      3. *-commutative 65.0%

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

      4. times-frac 65.0%

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

      5. associate-/l/ 65.0%

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

      6. *-commutative 65.0%

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

   10. Simplified 65.0%

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

   11. Taylor expanded in b around 0 87.7%

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

   if -3.99999999999999979e124 < (-.f64 t 1) < 3.99999999999999982e37

   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/ 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 82.4%

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

      6. *-commutative 82.4%

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

      7. exp-to-pow 83.3%

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

      8. sub-neg 83.3%

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

      9. metadata-eval 83.3%

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

      10. exp-diff 71.9%

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

      11. *-commutative 71.9%

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

      12. exp-to-pow 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in t around 0 76.5%

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

      1. times-frac 79.7%

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

   6. Simplified 79.7%

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

   if 3.99999999999999982e37 < (-.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/ 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 51.0%

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

      6. *-commutative 51.0%

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

      7. exp-to-pow 51.0%

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

      8. sub-neg 51.0%

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

      9. metadata-eval 51.0%

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

      10. exp-diff 49.0%

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

      11. *-commutative 49.0%

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

      12. exp-to-pow 49.0%

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

   3. Simplified 49.0%

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

   4. Taylor expanded in y around 0 73.6%

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

      1. times-frac 73.6%

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

      2. sub-neg 73.6%

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

      3. metadata-eval 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in b around 0 81.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -4 \cdot 10^{+124}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+37}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 7: 88.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+96} \lor \neg \left(y \leq 1.82 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.8e+96) (not (<= y 1.82e+137)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e+96) || !(y <= 1.82e+137)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.8d+96)) .or. (.not. (y <= 1.82d+137))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.8e+96) || !(y <= 1.82e+137)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.8e+96) or not (y <= 1.82e+137):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.8e+96) || !(y <= 1.82e+137))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.8e+96) || ~((y <= 1.82e+137)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.8e+96], N[Not[LessEqual[y, 1.82e+137]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000002e96 or 1.81999999999999999e137 < 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/ 86.0%

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

      2. *-commutative 86.0%

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

      3. +-commutative 86.0%

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

      4. associate--l+ 86.0%

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

      5. exp-sum 66.3%

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

      6. *-commutative 66.3%

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

      7. exp-to-pow 66.3%

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

      8. sub-neg 66.3%

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

      9. metadata-eval 66.3%

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

      10. exp-diff 51.2%

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

      11. *-commutative 51.2%

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

      12. exp-to-pow 51.2%

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

   3. Simplified 51.2%

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

   4. Taylor expanded in b around 0 64.0%

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

   5. Taylor expanded in t around 0 90.8%

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

   if -6.8000000000000002e96 < y < 1.81999999999999999e137

   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. Taylor expanded in y around 0 91.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+96} \lor \neg \left(y \leq 1.82 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 8: 73.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3900:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -3900.0)
     t_1
     (if (<= y -8e-203)
       (/ x (* y (* a (exp b))))
       (if (<= y 1.06e-90)
         (/ (* x (pow a t)) (* y a))
         (if (<= y 1.15e-14) (/ x (* (exp b) (* y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -3900.0) {
		tmp = t_1;
	} else if (y <= -8e-203) {
		tmp = x / (y * (a * exp(b)));
	} else if (y <= 1.06e-90) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 1.15e-14) {
		tmp = x / (exp(b) * (y * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-3900.0d0)) then
        tmp = t_1
    else if (y <= (-8d-203)) then
        tmp = x / (y * (a * exp(b)))
    else if (y <= 1.06d-90) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 1.15d-14) then
        tmp = x / (exp(b) * (y * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -3900.0) {
		tmp = t_1;
	} else if (y <= -8e-203) {
		tmp = x / (y * (a * Math.exp(b)));
	} else if (y <= 1.06e-90) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 1.15e-14) {
		tmp = x / (Math.exp(b) * (y * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -3900.0:
		tmp = t_1
	elif y <= -8e-203:
		tmp = x / (y * (a * math.exp(b)))
	elif y <= 1.06e-90:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 1.15e-14:
		tmp = x / (math.exp(b) * (y * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -3900.0)
		tmp = t_1;
	elseif (y <= -8e-203)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	elseif (y <= 1.06e-90)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 1.15e-14)
		tmp = Float64(x / Float64(exp(b) * Float64(y * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -3900.0)
		tmp = t_1;
	elseif (y <= -8e-203)
		tmp = x / (y * (a * exp(b)));
	elseif (y <= 1.06e-90)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 1.15e-14)
		tmp = x / (exp(b) * (y * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3900.0], t$95$1, If[LessEqual[y, -8e-203], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e-90], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-14], N[(x / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3900 or 1.14999999999999999e-14 < 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/ 90.8%

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

      2. *-commutative 90.8%

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

      3. +-commutative 90.8%

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

      4. associate--l+ 90.8%

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

      5. exp-sum 66.9%

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

      6. *-commutative 66.9%

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

      7. exp-to-pow 66.9%

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

      8. sub-neg 66.9%

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

      9. metadata-eval 66.9%

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

      10. exp-diff 51.5%

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

      11. *-commutative 51.5%

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

      12. exp-to-pow 51.5%

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

   3. Simplified 51.5%

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

   4. Taylor expanded in b around 0 60.9%

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

   5. Taylor expanded in t around 0 79.6%

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

   if -3900 < y < -8.0000000000000003e-203

   1. Initial program 95.9%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

      3. +-commutative 89.6%

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

      4. associate--l+ 89.6%

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

      5. exp-sum 78.3%

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

      6. *-commutative 78.3%

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

      7. exp-to-pow 79.8%

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

      8. sub-neg 79.8%

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

      9. metadata-eval 79.8%

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

      10. exp-diff 77.5%

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

      11. *-commutative 77.5%

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

      12. exp-to-pow 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in t around 0 76.9%

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

      1. times-frac 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in y around 0 81.4%

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

   if -8.0000000000000003e-203 < y < 1.0600000000000001e-90

   1. Initial program 94.5%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

      3. +-commutative 84.1%

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

      4. associate--l+ 84.1%

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

      5. exp-sum 74.3%

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

      6. *-commutative 74.3%

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

      7. exp-to-pow 75.4%

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

      8. sub-neg 75.4%

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

      9. metadata-eval 75.4%

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

      10. exp-diff 75.4%

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

      11. *-commutative 75.4%

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

      12. exp-to-pow 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. times-frac 78.6%

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

      2. sub-neg 78.6%

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

      3. metadata-eval 78.6%

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

   6. Simplified 78.6%

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

      1. expm1-log1p-u 53.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 46.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 51.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 51.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 54.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 80.5%

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

      3. *-commutative 80.5%

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

      4. times-frac 78.6%

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

      5. associate-/l/ 77.1%

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

      6. *-commutative 77.1%

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

   10. Simplified 77.1%

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

   11. Taylor expanded in b around 0 79.3%

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

   if 1.0600000000000001e-90 < y < 1.14999999999999999e-14

   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/ 94.0%

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

      2. *-commutative 94.0%

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

      3. +-commutative 94.0%

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

      4. associate--l+ 94.0%

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

      5. exp-sum 89.2%

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

      6. *-commutative 89.2%

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

      7. exp-to-pow 90.7%

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

      8. sub-neg 90.7%

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

      9. metadata-eval 90.7%

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

      10. exp-diff 90.7%

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

      11. *-commutative 90.7%

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

      12. exp-to-pow 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around 0 90.3%

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

      1. times-frac 90.7%

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

      2. sub-neg 90.7%

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

      3. metadata-eval 90.7%

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

   6. Simplified 90.7%

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

      1. expm1-log1p-u 71.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 66.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 65.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 65.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 65.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 65.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 65.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 65.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 70.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 90.3%

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

      3. *-commutative 90.3%

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

      4. times-frac 90.7%

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

      5. associate-/l/ 90.7%

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

      6. *-commutative 90.7%

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

   10. Simplified 90.7%

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

   11. Taylor expanded in t around 0 94.4%

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

       1. associate-*r* 94.4%

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

       2. *-commutative 94.4%

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

       3. *-commutative 94.4%

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

   13. Simplified 94.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3900:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 9: 70.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+148} \lor \neg \left(b \leq 0.011\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.8e+148) (not (<= b 0.011)))
   (/ x (* y (* a (exp b))))
   (/ (* x (pow a t)) (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.8e+148) || !(b <= 0.011)) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = (x * pow(a, t)) / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.8d+148)) .or. (.not. (b <= 0.011d0))) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = (x * (a ** t)) / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.8e+148) || !(b <= 0.011)) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, t)) / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.8e+148) or not (b <= 0.011):
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = (x * math.pow(a, t)) / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.8e+148) || !(b <= 0.011))
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.8e+148) || ~((b <= 0.011)))
		tmp = x / (y * (a * exp(b)));
	else
		tmp = (x * (a ^ t)) / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.8e+148], N[Not[LessEqual[b, 0.011]], $MachinePrecision]], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.7999999999999999e148 or 0.010999999999999999 < 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/ 91.2%

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

      2. *-commutative 91.2%

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

      3. +-commutative 91.2%

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

      4. associate--l+ 91.2%

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

      5. exp-sum 68.1%

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

      6. *-commutative 68.1%

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

      7. exp-to-pow 68.1%

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

      8. sub-neg 68.1%

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

      9. metadata-eval 68.1%

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

      10. exp-diff 56.0%

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

      11. *-commutative 56.0%

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

      12. exp-to-pow 56.0%

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

   3. Simplified 56.0%

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

   4. Taylor expanded in t around 0 74.8%

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

      1. times-frac 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in y around 0 90.3%

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

   if -5.7999999999999999e148 < b < 0.010999999999999999

   1. Initial program 96.6%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. +-commutative 88.2%

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

      4. associate--l+ 88.2%

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

      5. exp-sum 74.9%

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

      6. *-commutative 74.9%

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

      7. exp-to-pow 75.8%

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

      8. sub-neg 75.8%

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

      9. metadata-eval 75.8%

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

      10. exp-diff 69.8%

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

      11. *-commutative 69.8%

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

      12. exp-to-pow 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around 0 67.2%

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

      1. times-frac 66.1%

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

      2. sub-neg 66.1%

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

      3. metadata-eval 66.1%

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

   6. Simplified 66.1%

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

      1. expm1-log1p-u 37.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)\right)} \]

      2. expm1-udef 34.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\right)} - 1} \]

      3. frac-times 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}}\right)} - 1 \]

      4. metadata-eval 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\left(t + \color{blue}{\left(-1\right)}\right)} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      5. sub-neg 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{{a}^{\color{blue}{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}}\right)} - 1 \]

      6. *-commutative 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x \cdot {a}^{\left(t - 1\right)}}}{y \cdot e^{b}}\right)} - 1 \]

      7. pow-sub 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{y \cdot e^{b}}\right)} - 1 \]

      8. pow1 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{\color{blue}{a}}}{y \cdot e^{b}}\right)} - 1 \]

   8. Applied egg-rr 35.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 37.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \frac{{a}^{t}}{a}}{y \cdot e^{b}}\right)\right)} \]

      2. expm1-log1p 67.3%

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

      3. *-commutative 67.3%

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

      4. times-frac 66.2%

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

      5. associate-/l/ 61.3%

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

      6. *-commutative 61.3%

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

   10. Simplified 61.3%

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

   11. Taylor expanded in b around 0 66.1%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+148} \lor \neg \left(b \leq 0.011\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \end{array} \]

Alternative 10: 73.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{+149} \lor \neg \left(b \leq 0.011\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.26e+149) (not (<= b 0.011)))
   (/ x (* y (* a (exp b))))
   (/ (* x (pow a (+ t -1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.26e+149) || !(b <= 0.011)) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = (x * pow(a, (t + -1.0))) / 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 <= (-1.26d+149)) .or. (.not. (b <= 0.011d0))) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / 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 <= -1.26e+149) || !(b <= 0.011)) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.26e+149) or not (b <= 0.011):
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.26e+149) || !(b <= 0.011))
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.26e+149) || ~((b <= 0.011)))
		tmp = x / (y * (a * exp(b)));
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.26e+149], N[Not[LessEqual[b, 0.011]], $MachinePrecision]], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.26000000000000005e149 or 0.010999999999999999 < 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/ 91.2%

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

      2. *-commutative 91.2%

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

      3. +-commutative 91.2%

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

      4. associate--l+ 91.2%

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

      5. exp-sum 68.1%

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

      6. *-commutative 68.1%

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

      7. exp-to-pow 68.1%

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

      8. sub-neg 68.1%

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

      9. metadata-eval 68.1%

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

      10. exp-diff 56.0%

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

      11. *-commutative 56.0%

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

      12. exp-to-pow 56.0%

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

   3. Simplified 56.0%

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

   4. Taylor expanded in t around 0 74.8%

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

      1. times-frac 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in y around 0 90.3%

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

   if -1.26000000000000005e149 < b < 0.010999999999999999

   1. Initial program 96.6%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. +-commutative 88.2%

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

      4. associate--l+ 88.2%

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

      5. exp-sum 74.9%

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

      6. *-commutative 74.9%

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

      7. exp-to-pow 75.8%

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

      8. sub-neg 75.8%

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

      9. metadata-eval 75.8%

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

      10. exp-diff 69.8%

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

      11. *-commutative 69.8%

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

      12. exp-to-pow 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around 0 67.2%

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

      1. times-frac 66.1%

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

      2. sub-neg 66.1%

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

      3. metadata-eval 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in b around 0 70.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{+149} \lor \neg \left(b \leq 0.011\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 11: 59.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. associate-*l/ 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 72.5%

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

   6. *-commutative 72.5%

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

   7. exp-to-pow 73.1%

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

   8. sub-neg 73.1%

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

   9. metadata-eval 73.1%

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

   10. exp-diff 64.9%

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

   11. *-commutative 64.9%

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

   12. exp-to-pow 64.9%

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

3. Simplified 64.9%

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

4. Taylor expanded in t around 0 66.6%

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

   1. times-frac 68.7%

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

6. Simplified 68.7%

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

7. Taylor expanded in y around 0 59.9%

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

8. Final simplification 59.9%

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

Alternative 12: 43.7% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t_1 \cdot \left(1 - b\right) + t_1 \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -5.5e-8)
     (+ (* t_1 (- 1.0 b)) (* t_1 (* 0.5 (* b b))))
     (/ x (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -5.5e-8) {
		tmp = (t_1 * (1.0 - b)) + (t_1 * (0.5 * (b * b)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -5.5e-8) {
		tmp = (t_1 * (1.0 - b)) + (t_1 * (0.5 * (b * b)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -5.5e-8:
		tmp = (t_1 * (1.0 - b)) + (t_1 * (0.5 * (b * b)))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -5.5e-8)
		tmp = Float64(Float64(t_1 * Float64(1.0 - b)) + Float64(t_1 * Float64(0.5 * Float64(b * b))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -5.5e-8)
		tmp = (t_1 * (1.0 - b)) + (t_1 * (0.5 * (b * b)));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-8], N[(N[(t$95$1 * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000003e-8

   1. Initial program 99.7%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. +-commutative 94.1%

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

      4. associate--l+ 94.1%

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

      5. exp-sum 78.0%

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

      6. *-commutative 78.0%

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

      7. exp-to-pow 78.0%

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

      8. sub-neg 78.0%

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

      9. metadata-eval 78.0%

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

      10. exp-diff 53.0%

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

      11. *-commutative 53.0%

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

      12. exp-to-pow 53.0%

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

   3. Simplified 53.0%

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

   4. Taylor expanded in y around 0 67.8%

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

      1. times-frac 66.4%

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

      2. sub-neg 66.4%

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

      3. metadata-eval 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in t around 0 75.3%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 75.3%

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

      4. associate-/r* 71.0%

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

   9. Simplified 71.0%

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

   10. Taylor expanded in b around 0 46.9%

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

       1. +-commutative 46.9%

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

       2. +-commutative 46.9%

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

       3. metadata-eval 46.9%

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

       4. associate-/l* 51.0%

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

       5. associate-*r/ 49.6%

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

       6. cancel-sign-sub-inv 49.6%

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

       7. *-lft-identity 49.6%

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

       8. *-lft-identity 49.6%

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

       9. associate-*r/ 51.0%

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

       10. *-commutative 51.0%

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

       11. associate-/l* 46.9%

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

       12. associate-*r/ 51.0%

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

       13. distribute-rgt-out-- 51.0%

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

       14. mul-1-neg 51.0%

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

   12. Simplified 70.1%

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

   if -5.5000000000000003e-8 < 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. 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 70.5%

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

      6. *-commutative 70.5%

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

      7. exp-to-pow 71.3%

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

      8. sub-neg 71.3%

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

      9. metadata-eval 71.3%

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

      10. exp-diff 69.2%

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

      11. *-commutative 69.2%

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

      12. exp-to-pow 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in t around 0 68.8%

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

      1. times-frac 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in y around 0 54.3%

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

   8. Taylor expanded in b around 0 39.8%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right) + \frac{x}{y \cdot a} \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 13: 40.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-192}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e-192) (/ (- (/ x a) (/ x (/ a b))) y) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-192) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d-192)) then
        tmp = ((x / a) - (x / (a / b))) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-192) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e-192:
		tmp = ((x / a) - (x / (a / b))) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e-192)
		tmp = Float64(Float64(Float64(x / a) - Float64(x / Float64(a / b))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e-192)
		tmp = ((x / a) - (x / (a / b))) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e-192], N[(N[(N[(x / a), $MachinePrecision] - N[(x / N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.0000000000000001e-192

   1. Initial program 98.7%

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

      1. associate-*l/ 92.7%

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

      2. *-commutative 92.7%

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

      3. +-commutative 92.7%

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

      4. associate--l+ 92.7%

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

      5. exp-sum 76.9%

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

      6. *-commutative 76.9%

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

      7. exp-to-pow 77.2%

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

      8. sub-neg 77.2%

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

      9. metadata-eval 77.2%

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

      10. exp-diff 62.3%

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

      11. *-commutative 62.3%

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

      12. exp-to-pow 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in t around 0 61.6%

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

      1. times-frac 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in y around 0 60.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in y around 0 50.8%

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

       1. +-commutative 50.8%

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

       2. mul-1-neg 50.8%

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

       3. unsub-neg 50.8%

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

       4. *-commutative 50.8%

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

       5. associate-/l* 49.2%

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

   11. Simplified 49.2%

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

   if -5.0000000000000001e-192 < 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. Step-by-step derivation

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

      3. +-commutative 86.5%

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

      4. associate--l+ 86.5%

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

      5. exp-sum 68.9%

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

      6. *-commutative 68.9%

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

      7. exp-to-pow 69.8%

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

      8. sub-neg 69.8%

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

      9. metadata-eval 69.8%

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

      10. exp-diff 67.0%

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

      11. *-commutative 67.0%

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

      12. exp-to-pow 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. times-frac 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in y around 0 59.4%

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

   8. Taylor expanded in b around 0 40.3%

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

4. Final simplification 44.3%

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

Alternative 14: 41.0% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-192}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e-192) (/ (- (/ x y) (/ (* x b) y)) a) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-192) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d-192)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-192) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e-192:
		tmp = ((x / y) - ((x * b) / y)) / a
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e-192)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e-192)
		tmp = ((x / y) - ((x * b) / y)) / a;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e-192], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0000000000000002e-192

   1. Initial program 98.7%

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

      1. associate-*l/ 92.7%

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

      2. *-commutative 92.7%

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

      3. +-commutative 92.7%

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

      4. associate--l+ 92.7%

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

      5. exp-sum 76.9%

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

      6. *-commutative 76.9%

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

      7. exp-to-pow 77.2%

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

      8. sub-neg 77.2%

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

      9. metadata-eval 77.2%

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

      10. exp-diff 62.3%

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

      11. *-commutative 62.3%

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

      12. exp-to-pow 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in t around 0 61.6%

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

      1. times-frac 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in y around 0 60.4%

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

   8. Taylor expanded in b around 0 46.5%

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

   9. Taylor expanded in a around 0 49.4%

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

   if -2.0000000000000002e-192 < 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. Step-by-step derivation

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

      3. +-commutative 86.5%

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

      4. associate--l+ 86.5%

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

      5. exp-sum 68.9%

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

      6. *-commutative 68.9%

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

      7. exp-to-pow 69.8%

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

      8. sub-neg 69.8%

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

      9. metadata-eval 69.8%

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

      10. exp-diff 67.0%

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

      11. *-commutative 67.0%

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

      12. exp-to-pow 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. times-frac 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in y around 0 59.4%

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

   8. Taylor expanded in b around 0 40.3%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-192}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 15: 40.7% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{-\frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6e+27) (* x (/ (- (/ b a)) y)) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+27) {
		tmp = x * (-(b / a) / y);
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6d+27)) then
        tmp = x * (-(b / a) / y)
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+27) {
		tmp = x * (-(b / a) / y);
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6e+27:
		tmp = x * (-(b / a) / y)
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6e+27)
		tmp = Float64(x * Float64(Float64(-Float64(b / a)) / y));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6e+27)
		tmp = x * (-(b / a) / y);
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6e+27], N[(x * N[((-N[(b / a), $MachinePrecision]) / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.99999999999999953e27

   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/ 95.0%

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

      2. *-commutative 95.0%

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

      3. +-commutative 95.0%

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

      4. associate--l+ 95.0%

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

      5. exp-sum 81.7%

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

      6. *-commutative 81.7%

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

      7. exp-to-pow 81.7%

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

      8. sub-neg 81.7%

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

      9. metadata-eval 81.7%

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

      10. exp-diff 58.3%

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

      11. *-commutative 58.3%

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

      12. exp-to-pow 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in t around 0 65.1%

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

      1. times-frac 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in y around 0 82.0%

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

   8. Taylor expanded in b around 0 53.6%

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

   9. Taylor expanded in b around inf 53.6%

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

       1. associate-*r/ 53.6%

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

       2. *-commutative 53.6%

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

       3. neg-mul-1 53.6%

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

       4. distribute-frac-neg 53.6%

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

       5. associate-*r/ 50.6%

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

       6. *-commutative 50.6%

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

       7. distribute-rgt-neg-in 50.6%

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

       8. associate-/r* 53.8%

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

       9. distribute-neg-frac 53.8%

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

   11. Simplified 53.8%

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

   if -5.99999999999999953e27 < 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. 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 69.7%

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

      6. *-commutative 69.7%

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

      7. exp-to-pow 70.5%

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

      8. sub-neg 70.5%

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

      9. metadata-eval 70.5%

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

      10. exp-diff 66.9%

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

      11. *-commutative 66.9%

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

      12. exp-to-pow 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in t around 0 67.0%

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

      1. times-frac 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in y around 0 53.1%

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

   8. Taylor expanded in b around 0 39.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{-\frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 35.5% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;-x \cdot \frac{\frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e-55) (- (* x (/ (/ b a) y))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e-55) {
		tmp = -(x * ((b / a) / y));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.55d-55)) then
        tmp = -(x * ((b / a) / y))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e-55) {
		tmp = -(x * ((b / a) / y));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e-55:
		tmp = -(x * ((b / a) / y))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.55e-55)
		tmp = Float64(-Float64(x * Float64(Float64(b / a) / y)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.55e-55)
		tmp = -(x * ((b / a) / y));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.55e-55], (-N[(x * N[(N[(b / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.54999999999999998e-55

   1. Initial program 99.8%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

      3. +-commutative 93.6%

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

      4. associate--l+ 93.6%

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

      5. exp-sum 76.0%

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

      6. *-commutative 76.0%

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

      7. exp-to-pow 76.0%

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

      8. sub-neg 76.0%

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

      9. metadata-eval 76.0%

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

      10. exp-diff 54.5%

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

      11. *-commutative 54.5%

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

      12. exp-to-pow 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around 0 60.9%

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

      1. times-frac 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 67.7%

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

   8. Taylor expanded in b around 0 47.6%

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

   9. Taylor expanded in b around inf 46.7%

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

       1. associate-*r/ 46.7%

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

       2. *-commutative 46.7%

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

       3. neg-mul-1 46.7%

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

       4. distribute-frac-neg 46.7%

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

       5. associate-*r/ 44.5%

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

       6. *-commutative 44.5%

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

       7. distribute-rgt-neg-in 44.5%

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

       8. associate-/r* 45.7%

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

       9. distribute-neg-frac 45.7%

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

   11. Simplified 45.7%

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

   if -1.54999999999999998e-55 < b

   1. Initial program 97.0%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

      3. +-commutative 87.3%

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

      4. associate--l+ 87.3%

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

      5. exp-sum 70.9%

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

      6. *-commutative 70.9%

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

      7. exp-to-pow 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 69.5%

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

      11. *-commutative 69.5%

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

      12. exp-to-pow 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in t around 0 69.1%

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

      1. times-frac 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around 0 56.4%

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

   8. Taylor expanded in b around 0 35.6%

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

      1. *-commutative 35.6%

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

      2. associate-/r* 37.1%

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

   10. Simplified 37.1%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-55}:\\ \;\;\;\;-x \cdot \frac{\frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 17: 34.8% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e-54) (/ (* 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 <= -1e-54) {
		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 <= (-1d-54)) 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 <= -1e-54) {
		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 <= -1e-54:
		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 <= -1e-54)
		tmp = Float64(Float64(x * Float64(-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 <= -1e-54)
		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, -1e-54], 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 < -1e-54

   1. Initial program 99.8%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

      3. +-commutative 93.6%

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

      4. associate--l+ 93.6%

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

      5. exp-sum 76.0%

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

      6. *-commutative 76.0%

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

      7. exp-to-pow 76.0%

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

      8. sub-neg 76.0%

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

      9. metadata-eval 76.0%

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

      10. exp-diff 54.5%

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

      11. *-commutative 54.5%

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

      12. exp-to-pow 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around 0 60.9%

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

      1. times-frac 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 67.7%

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

   8. Taylor expanded in b around 0 47.6%

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

   9. Taylor expanded in b around inf 46.7%

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

   if -1e-54 < b

   1. Initial program 97.0%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

      3. +-commutative 87.3%

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

      4. associate--l+ 87.3%

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

      5. exp-sum 70.9%

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

      6. *-commutative 70.9%

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

      7. exp-to-pow 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 69.5%

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

      11. *-commutative 69.5%

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

      12. exp-to-pow 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in t around 0 69.1%

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

      1. times-frac 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around 0 56.4%

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

   8. Taylor expanded in b around 0 35.6%

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

      1. *-commutative 35.6%

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

      2. associate-/r* 37.1%

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

   10. Simplified 37.1%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 18: 31.9% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{a \cdot \frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (* a (/ y x))))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (a * (y / x));
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (a * (y / x))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

   1. associate-*l/ 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 72.5%

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

   6. *-commutative 72.5%

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

   7. exp-to-pow 73.1%

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

   8. sub-neg 73.1%

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

   9. metadata-eval 73.1%

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

   10. exp-diff 64.9%

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

   11. *-commutative 64.9%

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

   12. exp-to-pow 64.9%

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

3. Simplified 64.9%

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

4. Taylor expanded in t around 0 66.6%

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

   1. times-frac 68.7%

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

6. Simplified 68.7%

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

7. Taylor expanded in y around 0 59.9%

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

8. Taylor expanded in b around 0 34.6%

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

   1. clear-num 34.6%

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

   2. inv-pow 34.6%

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

   3. *-commutative 34.6%

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

   4. *-un-lft-identity 34.6%

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

   5. times-frac 36.2%

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

   6. /-rgt-identity 36.2%

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

10. Applied egg-rr 36.2%

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

    1. unpow-1 36.2%

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

12. Simplified 36.2%

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

13. Final simplification 36.2%

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

Alternative 19: 31.8% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. associate-*l/ 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 72.5%

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

   6. *-commutative 72.5%

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

   7. exp-to-pow 73.1%

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

   8. sub-neg 73.1%

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

   9. metadata-eval 73.1%

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

   10. exp-diff 64.9%

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

   11. *-commutative 64.9%

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

   12. exp-to-pow 64.9%

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

3. Simplified 64.9%

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

4. Taylor expanded in t around 0 66.6%

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

   1. times-frac 68.7%

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

6. Simplified 68.7%

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

7. Taylor expanded in y around 0 59.9%

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

8. Taylor expanded in b around 0 34.6%

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

9. Final simplification 34.6%

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

Alternative 20: 31.9% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 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 72.5%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 72.5%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 73.1%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 73.1%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 73.1%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 64.9%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 64.9%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 64.9%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 64.9%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

4. Taylor expanded in t around 0 66.6%

   \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]
5. Step-by-step derivation

   1. times-frac 68.7%

      \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

6. Simplified 68.7%

   \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

7. Taylor expanded in y around 0 59.9%

   \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

8. Taylor expanded in b around 0 34.6%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
9. Step-by-step derivation

   1. *-commutative 34.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

   2. associate-/r* 35.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

10. Simplified 35.1%

    \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

11. Final simplification 35.1%

    \[\leadsto \frac{\frac{x}{a}}{y} \]

Alternative 21: 31.7% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x y) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / y) / a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / y) / a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / y) / a;
}

Python

def code(x, y, z, t, a, b):
	return (x / y) / a

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / y) / a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / y) / a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 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 72.5%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 72.5%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 73.1%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 73.1%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 73.1%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 64.9%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 64.9%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 64.9%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 64.9%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

4. Taylor expanded in y around 0 67.6%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]
5. Step-by-step derivation

   1. times-frac 66.5%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)}}{y} \cdot \frac{x}{e^{b}}} \]

   2. sub-neg 66.5%

      \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \cdot \frac{x}{e^{b}} \]

   3. metadata-eval 66.5%

      \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y} \cdot \frac{x}{e^{b}} \]

6. Simplified 66.5%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}} \]

7. Taylor expanded in t around 0 59.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
8. Step-by-step derivation

   1. associate-*r* 56.7%

      \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   2. *-commutative 56.7%

      \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

   3. associate-*r* 59.9%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   4. associate-/r* 56.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a \cdot e^{b}}} \]

9. Simplified 56.9%

   \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a \cdot e^{b}}} \]

10. Taylor expanded in b around 0 35.8%

    \[\leadsto \frac{\frac{x}{y}}{\color{blue}{a}} \]

11. Final simplification 35.8%

    \[\leadsto \frac{\frac{x}{y}}{a} \]

Developer target: 72.1% 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 2023268 
(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))