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

Percentage Accurate: 98.3% → 98.3%

Time: 27.6s

Alternatives: 21

Speedup: 1.0×

• 47.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 2: 80.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ t_2 := x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y))
        (t_2 (* x (* (pow a (+ t -1.0)) (/ (pow z y) y)))))
   (if (<= b -1.65e+110)
     (/
      (* x (+ 1.0 (* b (+ (* b (+ 0.5 (* b -0.16666666666666666))) -1.0))))
      y)
     (if (<= b -3.9e+58)
       t_2
       (if (<= b -2.8e+29)
         t_1
         (if (<= b -5.8e-145)
           t_2
           (if (<= b -1.76e-152)
             (* (/ x a) (/ (pow a t) y))
             (if (<= b -1.7e-205)
               (* (/ (pow z y) a) (/ x y))
               (if (<= b 1.35e+44) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double t_2 = x * (pow(a, (t + -1.0)) * (pow(z, y) / y));
	double tmp;
	if (b <= -1.65e+110) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -3.9e+58) {
		tmp = t_2;
	} else if (b <= -2.8e+29) {
		tmp = t_1;
	} else if (b <= -5.8e-145) {
		tmp = t_2;
	} else if (b <= -1.76e-152) {
		tmp = (x / a) * (pow(a, t) / y);
	} else if (b <= -1.7e-205) {
		tmp = (pow(z, y) / a) * (x / y);
	} else if (b <= 1.35e+44) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    t_2 = x * ((a ** (t + (-1.0d0))) * ((z ** y) / y))
    if (b <= (-1.65d+110)) then
        tmp = (x * (1.0d0 + (b * ((b * (0.5d0 + (b * (-0.16666666666666666d0)))) + (-1.0d0))))) / y
    else if (b <= (-3.9d+58)) then
        tmp = t_2
    else if (b <= (-2.8d+29)) then
        tmp = t_1
    else if (b <= (-5.8d-145)) then
        tmp = t_2
    else if (b <= (-1.76d-152)) then
        tmp = (x / a) * ((a ** t) / y)
    else if (b <= (-1.7d-205)) then
        tmp = ((z ** y) / a) * (x / y)
    else if (b <= 1.35d+44) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double t_2 = x * (Math.pow(a, (t + -1.0)) * (Math.pow(z, y) / y));
	double tmp;
	if (b <= -1.65e+110) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -3.9e+58) {
		tmp = t_2;
	} else if (b <= -2.8e+29) {
		tmp = t_1;
	} else if (b <= -5.8e-145) {
		tmp = t_2;
	} else if (b <= -1.76e-152) {
		tmp = (x / a) * (Math.pow(a, t) / y);
	} else if (b <= -1.7e-205) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else if (b <= 1.35e+44) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	t_2 = x * (math.pow(a, (t + -1.0)) * (math.pow(z, y) / y))
	tmp = 0
	if b <= -1.65e+110:
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y
	elif b <= -3.9e+58:
		tmp = t_2
	elif b <= -2.8e+29:
		tmp = t_1
	elif b <= -5.8e-145:
		tmp = t_2
	elif b <= -1.76e-152:
		tmp = (x / a) * (math.pow(a, t) / y)
	elif b <= -1.7e-205:
		tmp = (math.pow(z, y) / a) * (x / y)
	elif b <= 1.35e+44:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	t_2 = Float64(x * Float64((a ^ Float64(t + -1.0)) * Float64((z ^ y) / y)))
	tmp = 0.0
	if (b <= -1.65e+110)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))) + -1.0)))) / y);
	elseif (b <= -3.9e+58)
		tmp = t_2;
	elseif (b <= -2.8e+29)
		tmp = t_1;
	elseif (b <= -5.8e-145)
		tmp = t_2;
	elseif (b <= -1.76e-152)
		tmp = Float64(Float64(x / a) * Float64((a ^ t) / y));
	elseif (b <= -1.7e-205)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	elseif (b <= 1.35e+44)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	t_2 = x * ((a ^ (t + -1.0)) * ((z ^ y) / y));
	tmp = 0.0;
	if (b <= -1.65e+110)
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	elseif (b <= -3.9e+58)
		tmp = t_2;
	elseif (b <= -2.8e+29)
		tmp = t_1;
	elseif (b <= -5.8e-145)
		tmp = t_2;
	elseif (b <= -1.76e-152)
		tmp = (x / a) * ((a ^ t) / y);
	elseif (b <= -1.7e-205)
		tmp = ((z ^ y) / a) * (x / y);
	elseif (b <= 1.35e+44)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+110], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.9e+58], t$95$2, If[LessEqual[b, -2.8e+29], t$95$1, If[LessEqual[b, -5.8e-145], t$95$2, If[LessEqual[b, -1.76e-152], N[(N[(x / a), $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-205], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+44], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.64999999999999986e110

   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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 87.5%

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

      4. fma-define 87.5%

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

      5. sub-neg 87.5%

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

      6. metadata-eval 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in b around inf 81.3%

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

      1. neg-mul-1 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in b around 0 74.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in x around 0 87.9%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}}{y} \]

   11. Taylor expanded in x around 0 93.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}{y}} \]

   if -1.64999999999999986e110 < b < -3.9000000000000001e58 or -2.8e29 < b < -5.79999999999999968e-145 or -1.7000000000000001e-205 < b < 1.35e44

   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* 96.3%

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

      2. associate--l+ 96.3%

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

      3. exp-sum 81.9%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 74.7%

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

      8. *-commutative 74.7%

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

      9. exp-to-pow 75.6%

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

      10. sub-neg 75.6%

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

      11. metadata-eval 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in b around 0 85.6%

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

      1. associate-/l* 85.6%

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

      2. exp-to-pow 86.4%

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

      3. sub-neg 86.4%

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

      4. metadata-eval 86.4%

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

   7. Simplified 86.4%

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

   if -3.9000000000000001e58 < b < -2.8e29 or 1.35e44 < 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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 85.7%

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

      4. fma-define 85.7%

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

      5. sub-neg 85.7%

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

      6. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around inf 76.9%

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

      1. neg-mul-1 76.9%

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

   7. Simplified 76.9%

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

      1. associate-*r/ 89.5%

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

   9. Applied egg-rr 89.5%

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

   10. Taylor expanded in b around inf 89.5%

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

       1. exp-neg 89.5%

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

       2. associate-*r/ 89.5%

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

       3. *-rgt-identity 89.5%

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

   12. Simplified 89.5%

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

   if -5.79999999999999968e-145 < b < -1.76000000000000001e-152

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 66.7%

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

      4. associate-/l* 66.7%

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

      5. *-commutative 66.7%

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

      6. exp-to-pow 66.7%

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

      7. exp-diff 66.7%

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

      8. *-commutative 66.7%

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

      9. exp-to-pow 66.7%

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

      10. sub-neg 66.7%

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

      11. metadata-eval 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. associate-/r* 100.0%

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

      2. exp-to-pow 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

      1. unpow-prod-up 100.0%

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

      2. unpow-1 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. associate-*r/ 100.0%

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

       2. *-rgt-identity 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in x around 0 100.0%

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

       1. times-frac 100.0%

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

   14. Simplified 100.0%

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

   15. Taylor expanded in b around 0 100.0%

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

   if -1.76000000000000001e-152 < b < -1.7000000000000001e-205

   1. Initial program 87.3%

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

      1. associate-/l* 88.0%

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

      2. associate--l+ 88.0%

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

      3. exp-sum 78.0%

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

      4. associate-/l* 78.0%

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

      5. *-commutative 78.0%

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

      6. exp-to-pow 78.0%

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

      7. exp-diff 78.0%

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

      8. *-commutative 78.0%

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

      9. exp-to-pow 80.3%

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

      10. sub-neg 80.3%

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

      11. metadata-eval 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in t around 0 80.5%

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

   6. Taylor expanded in b around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. times-frac 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -950000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-30}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{t\_1}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -950000000000.0)
     t_2
     (if (<= y -1.45e-21)
       (/ x (* a t_1))
       (if (<= y 4e-30) (/ (* x (/ (pow a t) t_1)) a) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -950000000000.0) {
		tmp = t_2;
	} else if (y <= -1.45e-21) {
		tmp = x / (a * t_1);
	} else if (y <= 4e-30) {
		tmp = (x * (pow(a, t) / t_1)) / a;
	} 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 = y * exp(b)
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-950000000000.0d0)) then
        tmp = t_2
    else if (y <= (-1.45d-21)) then
        tmp = x / (a * t_1)
    else if (y <= 4d-30) then
        tmp = (x * ((a ** t) / t_1)) / a
    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 = y * Math.exp(b);
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -950000000000.0) {
		tmp = t_2;
	} else if (y <= -1.45e-21) {
		tmp = x / (a * t_1);
	} else if (y <= 4e-30) {
		tmp = (x * (Math.pow(a, t) / t_1)) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -950000000000.0:
		tmp = t_2
	elif y <= -1.45e-21:
		tmp = x / (a * t_1)
	elif y <= 4e-30:
		tmp = (x * (math.pow(a, t) / t_1)) / a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -950000000000.0)
		tmp = t_2;
	elseif (y <= -1.45e-21)
		tmp = Float64(x / Float64(a * t_1));
	elseif (y <= 4e-30)
		tmp = Float64(Float64(x * Float64((a ^ t) / t_1)) / a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -950000000000.0)
		tmp = t_2;
	elseif (y <= -1.45e-21)
		tmp = x / (a * t_1);
	elseif (y <= 4e-30)
		tmp = (x * ((a ^ t) / t_1)) / a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -950000000000.0], t$95$2, If[LessEqual[y, -1.45e-21], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-30], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5e11 or 4e-30 < y

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 66.9%

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

      4. associate-/l* 65.4%

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

      5. *-commutative 65.4%

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

      6. exp-to-pow 65.4%

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

      7. exp-diff 57.5%

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

      8. *-commutative 57.5%

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

      9. exp-to-pow 57.5%

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

      10. sub-neg 57.5%

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

      11. metadata-eval 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in t around 0 63.1%

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

   6. Taylor expanded in b around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. times-frac 70.4%

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

   8. Simplified 70.4%

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

      1. associate-*l/ 80.7%

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

   10. Applied egg-rr 80.7%

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

   if -9.5e11 < y < -1.45e-21

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 80.0%

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

      4. associate-/l* 80.0%

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

      5. *-commutative 80.0%

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

      6. exp-to-pow 80.0%

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

      7. exp-diff 70.0%

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

      8. *-commutative 70.0%

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

      9. exp-to-pow 70.0%

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

      10. sub-neg 70.0%

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

      11. metadata-eval 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in y around 0 80.5%

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

      1. associate-/r* 70.5%

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

      2. exp-to-pow 70.5%

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

      3. sub-neg 70.5%

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

      4. metadata-eval 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in t around 0 90.5%

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

   if -1.45e-21 < y < 4e-30

   1. Initial program 97.4%

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

      1. associate-/l* 94.6%

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

      2. associate--l+ 94.6%

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

      3. exp-sum 94.6%

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

      4. associate-/l* 94.6%

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

      5. *-commutative 94.6%

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

      6. exp-to-pow 94.6%

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

      7. exp-diff 87.1%

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

      8. *-commutative 87.1%

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

      9. exp-to-pow 88.3%

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

      10. sub-neg 88.3%

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

      11. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around 0 87.1%

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

      1. associate-/r* 83.7%

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

      2. exp-to-pow 85.0%

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

      3. sub-neg 85.0%

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

      4. metadata-eval 85.0%

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

   7. Simplified 85.0%

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

      1. unpow-prod-up 85.0%

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

      2. unpow-1 85.0%

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

   9. Applied egg-rr 85.0%

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

       1. associate-*r/ 85.0%

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

       2. *-rgt-identity 85.0%

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

   11. Simplified 85.0%

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

   12. Taylor expanded in x around 0 87.3%

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

       1. times-frac 87.3%

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

   14. Simplified 87.3%

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

       1. associate-*l/ 90.0%

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

   16. Applied egg-rr 90.0%

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

Alternative 4: 88.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2100000000000 \lor \neg \left(y \leq 4.5 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2100000000000.0) (not (<= y 4.5e+79)))
   (/ (* 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 <= -2100000000000.0) || !(y <= 4.5e+79)) {
		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 <= (-2100000000000.0d0)) .or. (.not. (y <= 4.5d+79))) 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 <= -2100000000000.0) || !(y <= 4.5e+79)) {
		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 <= -2100000000000.0) or not (y <= 4.5e+79):
		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 <= -2100000000000.0) || !(y <= 4.5e+79))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2100000000000.0) || ~((y <= 4.5e+79)))
		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, -2100000000000.0], N[Not[LessEqual[y, 4.5e+79]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $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 < -2.1e12 or 4.49999999999999994e79 < y

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 66.4%

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

      4. associate-/l* 64.5%

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

      5. *-commutative 64.5%

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

      6. exp-to-pow 64.5%

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

      7. exp-diff 57.0%

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

      8. *-commutative 57.0%

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

      9. exp-to-pow 57.0%

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

      10. sub-neg 57.0%

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

      11. metadata-eval 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in t around 0 63.6%

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

   6. Taylor expanded in b around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. times-frac 72.2%

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

   8. Simplified 72.2%

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

      1. associate-*l/ 84.4%

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

   10. Applied egg-rr 84.4%

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

   if -2.1e12 < y < 4.49999999999999994e79

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-/l* 92.2%

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

      3. associate--l+ 92.2%

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

      4. fma-define 92.2%

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

      5. sub-neg 92.2%

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

      6. metadata-eval 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 96.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2100000000000 \lor \neg \left(y \leq 4.5 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ t_2 := \frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ t_3 := \frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;b \leq -7 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-194}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 0.12:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y))
        (t_2 (* (/ (pow z y) a) (/ x y)))
        (t_3 (* (/ x a) (/ (pow a t) y))))
   (if (<= b -7e+109)
     (/
      (* x (+ 1.0 (* b (+ (* b (+ 0.5 (* b -0.16666666666666666))) -1.0))))
      y)
     (if (<= b -1.6e+80)
       t_2
       (if (<= b -3.2e+20)
         t_1
         (if (<= b 4.7e-299)
           t_2
           (if (<= b 4.4e-194)
             t_3
             (if (<= b 1.5e-151)
               t_2
               (if (<= b 0.12)
                 t_3
                 (if (<= b 1.12e+104)
                   (/ x (* a (* y (exp b))))
                   (if (<= b 1.05e+106)
                     t_3
                     (if (<= b 9.2e+126) t_2 t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double t_2 = (pow(z, y) / a) * (x / y);
	double t_3 = (x / a) * (pow(a, t) / y);
	double tmp;
	if (b <= -7e+109) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -1.6e+80) {
		tmp = t_2;
	} else if (b <= -3.2e+20) {
		tmp = t_1;
	} else if (b <= 4.7e-299) {
		tmp = t_2;
	} else if (b <= 4.4e-194) {
		tmp = t_3;
	} else if (b <= 1.5e-151) {
		tmp = t_2;
	} else if (b <= 0.12) {
		tmp = t_3;
	} else if (b <= 1.12e+104) {
		tmp = x / (a * (y * exp(b)));
	} else if (b <= 1.05e+106) {
		tmp = t_3;
	} else if (b <= 9.2e+126) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / exp(b)) / y
    t_2 = ((z ** y) / a) * (x / y)
    t_3 = (x / a) * ((a ** t) / y)
    if (b <= (-7d+109)) then
        tmp = (x * (1.0d0 + (b * ((b * (0.5d0 + (b * (-0.16666666666666666d0)))) + (-1.0d0))))) / y
    else if (b <= (-1.6d+80)) then
        tmp = t_2
    else if (b <= (-3.2d+20)) then
        tmp = t_1
    else if (b <= 4.7d-299) then
        tmp = t_2
    else if (b <= 4.4d-194) then
        tmp = t_3
    else if (b <= 1.5d-151) then
        tmp = t_2
    else if (b <= 0.12d0) then
        tmp = t_3
    else if (b <= 1.12d+104) then
        tmp = x / (a * (y * exp(b)))
    else if (b <= 1.05d+106) then
        tmp = t_3
    else if (b <= 9.2d+126) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / Math.exp(b)) / y;
	double t_2 = (Math.pow(z, y) / a) * (x / y);
	double t_3 = (x / a) * (Math.pow(a, t) / y);
	double tmp;
	if (b <= -7e+109) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -1.6e+80) {
		tmp = t_2;
	} else if (b <= -3.2e+20) {
		tmp = t_1;
	} else if (b <= 4.7e-299) {
		tmp = t_2;
	} else if (b <= 4.4e-194) {
		tmp = t_3;
	} else if (b <= 1.5e-151) {
		tmp = t_2;
	} else if (b <= 0.12) {
		tmp = t_3;
	} else if (b <= 1.12e+104) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (b <= 1.05e+106) {
		tmp = t_3;
	} else if (b <= 9.2e+126) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	t_2 = (math.pow(z, y) / a) * (x / y)
	t_3 = (x / a) * (math.pow(a, t) / y)
	tmp = 0
	if b <= -7e+109:
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y
	elif b <= -1.6e+80:
		tmp = t_2
	elif b <= -3.2e+20:
		tmp = t_1
	elif b <= 4.7e-299:
		tmp = t_2
	elif b <= 4.4e-194:
		tmp = t_3
	elif b <= 1.5e-151:
		tmp = t_2
	elif b <= 0.12:
		tmp = t_3
	elif b <= 1.12e+104:
		tmp = x / (a * (y * math.exp(b)))
	elif b <= 1.05e+106:
		tmp = t_3
	elif b <= 9.2e+126:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	t_2 = Float64(Float64((z ^ y) / a) * Float64(x / y))
	t_3 = Float64(Float64(x / a) * Float64((a ^ t) / y))
	tmp = 0.0
	if (b <= -7e+109)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))) + -1.0)))) / y);
	elseif (b <= -1.6e+80)
		tmp = t_2;
	elseif (b <= -3.2e+20)
		tmp = t_1;
	elseif (b <= 4.7e-299)
		tmp = t_2;
	elseif (b <= 4.4e-194)
		tmp = t_3;
	elseif (b <= 1.5e-151)
		tmp = t_2;
	elseif (b <= 0.12)
		tmp = t_3;
	elseif (b <= 1.12e+104)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (b <= 1.05e+106)
		tmp = t_3;
	elseif (b <= 9.2e+126)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	t_2 = ((z ^ y) / a) * (x / y);
	t_3 = (x / a) * ((a ^ t) / y);
	tmp = 0.0;
	if (b <= -7e+109)
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	elseif (b <= -1.6e+80)
		tmp = t_2;
	elseif (b <= -3.2e+20)
		tmp = t_1;
	elseif (b <= 4.7e-299)
		tmp = t_2;
	elseif (b <= 4.4e-194)
		tmp = t_3;
	elseif (b <= 1.5e-151)
		tmp = t_2;
	elseif (b <= 0.12)
		tmp = t_3;
	elseif (b <= 1.12e+104)
		tmp = x / (a * (y * exp(b)));
	elseif (b <= 1.05e+106)
		tmp = t_3;
	elseif (b <= 9.2e+126)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / a), $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+109], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.6e+80], t$95$2, If[LessEqual[b, -3.2e+20], t$95$1, If[LessEqual[b, 4.7e-299], t$95$2, If[LessEqual[b, 4.4e-194], t$95$3, If[LessEqual[b, 1.5e-151], t$95$2, If[LessEqual[b, 0.12], t$95$3, If[LessEqual[b, 1.12e+104], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+106], t$95$3, If[LessEqual[b, 9.2e+126], t$95$2, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.99999999999999966e109

   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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 87.5%

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

      4. fma-define 87.5%

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

      5. sub-neg 87.5%

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

      6. metadata-eval 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in b around inf 81.3%

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

      1. neg-mul-1 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in b around 0 74.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in x around 0 87.9%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}}{y} \]

   11. Taylor expanded in x around 0 93.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}{y}} \]

   if -6.99999999999999966e109 < b < -1.59999999999999995e80 or -3.2e20 < b < 4.6999999999999997e-299 or 4.4000000000000003e-194 < b < 1.5e-151 or 1.05000000000000002e106 < b < 9.2000000000000002e126

   1. Initial program 97.6%

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

      1. associate-/l* 95.9%

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

      2. associate--l+ 95.9%

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

      3. exp-sum 81.5%

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

      4. associate-/l* 80.5%

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

      5. *-commutative 80.5%

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

      6. exp-to-pow 80.5%

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

      7. exp-diff 75.3%

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

      8. *-commutative 75.3%

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

      9. exp-to-pow 76.3%

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

      10. sub-neg 76.3%

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

      11. metadata-eval 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in t around 0 65.4%

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

   6. Taylor expanded in b around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. times-frac 76.6%

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

   8. Simplified 76.6%

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

   if -1.59999999999999995e80 < b < -3.2e20 or 9.2000000000000002e126 < 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. *-commutative 100.0%

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

      2. associate-/l* 87.8%

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

      3. associate--l+ 87.8%

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

      4. fma-define 87.8%

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

      5. sub-neg 87.8%

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

      6. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf 77.6%

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

      1. neg-mul-1 77.6%

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

   7. Simplified 77.6%

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

      1. associate-*r/ 90.0%

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

   9. Applied egg-rr 90.0%

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

   10. Taylor expanded in b around inf 90.0%

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

       1. exp-neg 90.0%

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

       2. associate-*r/ 90.0%

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

       3. *-rgt-identity 90.0%

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

   12. Simplified 90.0%

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

   if 4.6999999999999997e-299 < b < 4.4000000000000003e-194 or 1.5e-151 < b < 0.12 or 1.12000000000000003e104 < b < 1.05000000000000002e106

   1. Initial program 98.3%

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

      1. associate-/l* 94.6%

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

      2. associate--l+ 94.6%

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

      3. exp-sum 85.7%

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

      4. associate-/l* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 84.6%

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

      10. sub-neg 84.6%

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

      11. metadata-eval 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in y around 0 79.5%

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

      1. associate-/r* 79.5%

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

      2. exp-to-pow 80.6%

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

      3. sub-neg 80.6%

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

      4. metadata-eval 80.6%

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

   7. Simplified 80.6%

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

      1. unpow-prod-up 80.6%

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

      2. unpow-1 80.6%

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

   9. Applied egg-rr 80.6%

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

       1. associate-*r/ 80.6%

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

       2. *-rgt-identity 80.6%

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

   11. Simplified 80.6%

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

   12. Taylor expanded in x around 0 80.7%

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

       1. times-frac 80.3%

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

   14. Simplified 80.3%

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

   15. Taylor expanded in b around 0 82.5%

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

   if 0.12 < b < 1.12000000000000003e104

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 58.8%

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

      4. associate-/l* 58.8%

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

      5. *-commutative 58.8%

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

      6. exp-to-pow 58.8%

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

      7. exp-diff 41.2%

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

      8. *-commutative 41.2%

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

      9. exp-to-pow 41.2%

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

      10. sub-neg 41.2%

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

      11. metadata-eval 41.2%

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

   3. Simplified 41.2%

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

   5. Taylor expanded in y around 0 47.5%

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

      1. associate-/r* 35.8%

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

      2. exp-to-pow 35.8%

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

      3. sub-neg 35.8%

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

      4. metadata-eval 35.8%

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

   7. Simplified 35.8%

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

   8. Taylor expanded in t around 0 59.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 0.12:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ t_3 := \frac{{a}^{t}}{y}\\ \mathbf{if}\;y \leq -2900000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot t\_3}{a}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{a} \cdot t\_3\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b)))))
        (t_2 (* (/ (pow z y) a) (/ x y)))
        (t_3 (/ (pow a t) y)))
   (if (<= y -2900000000000.0)
     t_2
     (if (<= y -1.16e-57)
       t_1
       (if (<= y -1.35e-185)
         (/ (* x t_3) a)
         (if (<= y -8.4e-237)
           t_1
           (if (<= y -5.5e-290)
             (* (/ x a) t_3)
             (if (<= y 4.2e+124)
               t_1
               (if (<= y 2.65e+295) t_2 (/ (/ x (exp b)) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = (pow(z, y) / a) * (x / y);
	double t_3 = pow(a, t) / y;
	double tmp;
	if (y <= -2900000000000.0) {
		tmp = t_2;
	} else if (y <= -1.16e-57) {
		tmp = t_1;
	} else if (y <= -1.35e-185) {
		tmp = (x * t_3) / a;
	} else if (y <= -8.4e-237) {
		tmp = t_1;
	} else if (y <= -5.5e-290) {
		tmp = (x / a) * t_3;
	} else if (y <= 4.2e+124) {
		tmp = t_1;
	} else if (y <= 2.65e+295) {
		tmp = t_2;
	} else {
		tmp = (x / exp(b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (a * (y * exp(b)))
    t_2 = ((z ** y) / a) * (x / y)
    t_3 = (a ** t) / y
    if (y <= (-2900000000000.0d0)) then
        tmp = t_2
    else if (y <= (-1.16d-57)) then
        tmp = t_1
    else if (y <= (-1.35d-185)) then
        tmp = (x * t_3) / a
    else if (y <= (-8.4d-237)) then
        tmp = t_1
    else if (y <= (-5.5d-290)) then
        tmp = (x / a) * t_3
    else if (y <= 4.2d+124) then
        tmp = t_1
    else if (y <= 2.65d+295) then
        tmp = t_2
    else
        tmp = (x / exp(b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * Math.exp(b)));
	double t_2 = (Math.pow(z, y) / a) * (x / y);
	double t_3 = Math.pow(a, t) / y;
	double tmp;
	if (y <= -2900000000000.0) {
		tmp = t_2;
	} else if (y <= -1.16e-57) {
		tmp = t_1;
	} else if (y <= -1.35e-185) {
		tmp = (x * t_3) / a;
	} else if (y <= -8.4e-237) {
		tmp = t_1;
	} else if (y <= -5.5e-290) {
		tmp = (x / a) * t_3;
	} else if (y <= 4.2e+124) {
		tmp = t_1;
	} else if (y <= 2.65e+295) {
		tmp = t_2;
	} else {
		tmp = (x / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = (math.pow(z, y) / a) * (x / y)
	t_3 = math.pow(a, t) / y
	tmp = 0
	if y <= -2900000000000.0:
		tmp = t_2
	elif y <= -1.16e-57:
		tmp = t_1
	elif y <= -1.35e-185:
		tmp = (x * t_3) / a
	elif y <= -8.4e-237:
		tmp = t_1
	elif y <= -5.5e-290:
		tmp = (x / a) * t_3
	elif y <= 4.2e+124:
		tmp = t_1
	elif y <= 2.65e+295:
		tmp = t_2
	else:
		tmp = (x / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64(Float64((z ^ y) / a) * Float64(x / y))
	t_3 = Float64((a ^ t) / y)
	tmp = 0.0
	if (y <= -2900000000000.0)
		tmp = t_2;
	elseif (y <= -1.16e-57)
		tmp = t_1;
	elseif (y <= -1.35e-185)
		tmp = Float64(Float64(x * t_3) / a);
	elseif (y <= -8.4e-237)
		tmp = t_1;
	elseif (y <= -5.5e-290)
		tmp = Float64(Float64(x / a) * t_3);
	elseif (y <= 4.2e+124)
		tmp = t_1;
	elseif (y <= 2.65e+295)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = ((z ^ y) / a) * (x / y);
	t_3 = (a ^ t) / y;
	tmp = 0.0;
	if (y <= -2900000000000.0)
		tmp = t_2;
	elseif (y <= -1.16e-57)
		tmp = t_1;
	elseif (y <= -1.35e-185)
		tmp = (x * t_3) / a;
	elseif (y <= -8.4e-237)
		tmp = t_1;
	elseif (y <= -5.5e-290)
		tmp = (x / a) * t_3;
	elseif (y <= 4.2e+124)
		tmp = t_1;
	elseif (y <= 2.65e+295)
		tmp = t_2;
	else
		tmp = (x / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2900000000000.0], t$95$2, If[LessEqual[y, -1.16e-57], t$95$1, If[LessEqual[y, -1.35e-185], N[(N[(x * t$95$3), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -8.4e-237], t$95$1, If[LessEqual[y, -5.5e-290], N[(N[(x / a), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[y, 4.2e+124], t$95$1, If[LessEqual[y, 2.65e+295], t$95$2, N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.9e12 or 4.20000000000000023e124 < y < 2.6499999999999998e295

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 67.8%

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

      4. associate-/l* 65.5%

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

      5. *-commutative 65.5%

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

      6. exp-to-pow 65.5%

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

      7. exp-diff 58.6%

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

      8. *-commutative 58.6%

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

      9. exp-to-pow 58.6%

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

      10. sub-neg 58.6%

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

      11. metadata-eval 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in t around 0 66.7%

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

   6. Taylor expanded in b around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. times-frac 77.2%

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

   8. Simplified 77.2%

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

   if -2.9e12 < y < -1.15999999999999996e-57 or -1.34999999999999994e-185 < y < -8.4000000000000005e-237 or -5.5e-290 < y < 4.20000000000000023e124

   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* 96.9%

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

      2. associate--l+ 96.9%

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

      3. exp-sum 84.6%

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

      4. associate-/l* 84.6%

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

      5. *-commutative 84.6%

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

      6. exp-to-pow 84.6%

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

      7. exp-diff 75.3%

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

      8. *-commutative 75.3%

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

      9. exp-to-pow 76.2%

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

      10. sub-neg 76.2%

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

      11. metadata-eval 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in y around 0 81.7%

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

      1. associate-/r* 77.8%

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

      2. exp-to-pow 78.7%

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

      3. sub-neg 78.7%

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

      4. metadata-eval 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in t around 0 75.1%

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

   if -1.15999999999999996e-57 < y < -1.34999999999999994e-185

   1. Initial program 98.8%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 98.8%

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

      4. associate-/l* 98.8%

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

      5. *-commutative 98.8%

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

      6. exp-to-pow 98.8%

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

      7. exp-diff 90.1%

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

      8. *-commutative 90.1%

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

      9. exp-to-pow 91.2%

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

      10. sub-neg 91.2%

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

      11. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 90.1%

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

      1. associate-/r* 90.1%

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

      2. exp-to-pow 91.2%

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

      3. sub-neg 91.2%

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

      4. metadata-eval 91.2%

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

   7. Simplified 91.2%

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

      1. unpow-prod-up 91.2%

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

      2. unpow-1 91.2%

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

   9. Applied egg-rr 91.2%

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

       1. associate-*r/ 91.2%

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

       2. *-rgt-identity 91.2%

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

   11. Simplified 91.2%

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

   12. Taylor expanded in x around 0 91.3%

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

       1. times-frac 86.9%

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

   14. Simplified 86.9%

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

       1. associate-*l/ 87.2%

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

   16. Applied egg-rr 87.2%

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

   17. Taylor expanded in b around 0 87.6%

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

       1. associate-/l* 87.6%

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

   19. Simplified 87.6%

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

   if -8.4000000000000005e-237 < y < -5.5e-290

   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* 83.0%

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

      2. associate--l+ 83.0%

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

      3. exp-sum 83.0%

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

      4. associate-/l* 83.0%

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

      5. *-commutative 83.0%

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

      6. exp-to-pow 83.0%

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

      7. exp-diff 83.0%

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

      8. *-commutative 83.0%

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

      9. exp-to-pow 83.9%

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

      10. sub-neg 83.9%

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

      11. metadata-eval 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in y around 0 83.0%

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

      1. associate-/r* 83.0%

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

      2. exp-to-pow 83.9%

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

      3. sub-neg 83.9%

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

      4. metadata-eval 83.9%

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

   7. Simplified 83.9%

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

      1. unpow-prod-up 84.3%

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

      2. unpow-1 84.3%

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

   9. Applied egg-rr 84.3%

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

       1. associate-*r/ 84.3%

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

       2. *-rgt-identity 84.3%

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

   11. Simplified 84.3%

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

   12. Taylor expanded in x around 0 74.8%

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

       1. times-frac 91.3%

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

   14. Simplified 91.3%

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

   15. Taylor expanded in b around 0 91.5%

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

   if 2.6499999999999998e295 < 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. *-commutative 100.0%

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

      2. associate-/l* 50.0%

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

      3. associate--l+ 50.0%

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

      4. fma-define 50.0%

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

      5. sub-neg 50.0%

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

      6. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in b around inf 50.0%

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

      1. neg-mul-1 50.0%

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

   7. Simplified 50.0%

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

      1. associate-*r/ 100.0%

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

   9. Applied egg-rr 100.0%

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

   10. Taylor expanded in b around inf 100.0%

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

       1. exp-neg 100.0%

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

       2. associate-*r/ 100.0%

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

       3. *-rgt-identity 100.0%

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

   12. Simplified 100.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2900000000000:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{y}}{a}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+295}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -7000:\\ \;\;\;\;\frac{x}{a} \cdot t\_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t\_2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)) (t_2 (/ (pow a t) y)))
   (if (<= t -7000.0)
     (* (/ x a) t_2)
     (if (<= t -4.2e-30)
       (/ x (* a (* y (exp b))))
       (if (<= t -5.2e-141)
         t_1
         (if (<= t -3e-183)
           (/ (/ x (exp b)) y)
           (if (<= t 2.8e-298)
             t_1
             (if (<= t 1.55e+16)
               (/ (* x (/ (exp (- b)) y)) a)
               (/ (* x t_2) a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double t_2 = pow(a, t) / y;
	double tmp;
	if (t <= -7000.0) {
		tmp = (x / a) * t_2;
	} else if (t <= -4.2e-30) {
		tmp = x / (a * (y * exp(b)));
	} else if (t <= -5.2e-141) {
		tmp = t_1;
	} else if (t <= -3e-183) {
		tmp = (x / exp(b)) / y;
	} else if (t <= 2.8e-298) {
		tmp = t_1;
	} else if (t <= 1.55e+16) {
		tmp = (x * (exp(-b) / y)) / a;
	} else {
		tmp = (x * t_2) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    t_2 = (a ** t) / y
    if (t <= (-7000.0d0)) then
        tmp = (x / a) * t_2
    else if (t <= (-4.2d-30)) then
        tmp = x / (a * (y * exp(b)))
    else if (t <= (-5.2d-141)) then
        tmp = t_1
    else if (t <= (-3d-183)) then
        tmp = (x / exp(b)) / y
    else if (t <= 2.8d-298) then
        tmp = t_1
    else if (t <= 1.55d+16) then
        tmp = (x * (exp(-b) / y)) / a
    else
        tmp = (x * t_2) / 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 t_1 = (x * (Math.pow(z, y) / a)) / y;
	double t_2 = Math.pow(a, t) / y;
	double tmp;
	if (t <= -7000.0) {
		tmp = (x / a) * t_2;
	} else if (t <= -4.2e-30) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t <= -5.2e-141) {
		tmp = t_1;
	} else if (t <= -3e-183) {
		tmp = (x / Math.exp(b)) / y;
	} else if (t <= 2.8e-298) {
		tmp = t_1;
	} else if (t <= 1.55e+16) {
		tmp = (x * (Math.exp(-b) / y)) / a;
	} else {
		tmp = (x * t_2) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	t_2 = math.pow(a, t) / y
	tmp = 0
	if t <= -7000.0:
		tmp = (x / a) * t_2
	elif t <= -4.2e-30:
		tmp = x / (a * (y * math.exp(b)))
	elif t <= -5.2e-141:
		tmp = t_1
	elif t <= -3e-183:
		tmp = (x / math.exp(b)) / y
	elif t <= 2.8e-298:
		tmp = t_1
	elif t <= 1.55e+16:
		tmp = (x * (math.exp(-b) / y)) / a
	else:
		tmp = (x * t_2) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	t_2 = Float64((a ^ t) / y)
	tmp = 0.0
	if (t <= -7000.0)
		tmp = Float64(Float64(x / a) * t_2);
	elseif (t <= -4.2e-30)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t <= -5.2e-141)
		tmp = t_1;
	elseif (t <= -3e-183)
		tmp = Float64(Float64(x / exp(b)) / y);
	elseif (t <= 2.8e-298)
		tmp = t_1;
	elseif (t <= 1.55e+16)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / y)) / a);
	else
		tmp = Float64(Float64(x * t_2) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	t_2 = (a ^ t) / y;
	tmp = 0.0;
	if (t <= -7000.0)
		tmp = (x / a) * t_2;
	elseif (t <= -4.2e-30)
		tmp = x / (a * (y * exp(b)));
	elseif (t <= -5.2e-141)
		tmp = t_1;
	elseif (t <= -3e-183)
		tmp = (x / exp(b)) / y;
	elseif (t <= 2.8e-298)
		tmp = t_1;
	elseif (t <= 1.55e+16)
		tmp = (x * (exp(-b) / y)) / a;
	else
		tmp = (x * t_2) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -7000.0], N[(N[(x / a), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[t, -4.2e-30], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-141], t$95$1, If[LessEqual[t, -3e-183], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.8e-298], t$95$1, If[LessEqual[t, 1.55e+16], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * t$95$2), $MachinePrecision] / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7e3

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 81.4%

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

      4. associate-/l* 81.4%

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

      5. *-commutative 81.4%

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

      6. exp-to-pow 81.4%

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

      7. exp-diff 67.8%

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

      8. *-commutative 67.8%

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

      9. exp-to-pow 67.8%

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

      10. sub-neg 67.8%

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

      11. metadata-eval 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in y around 0 78.0%

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

      1. associate-/r* 78.0%

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

      2. exp-to-pow 78.0%

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

      3. sub-neg 78.0%

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

      4. metadata-eval 78.0%

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

   7. Simplified 78.0%

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

      1. unpow-prod-up 78.0%

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

      2. unpow-1 78.0%

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

   9. Applied egg-rr 78.0%

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

       1. associate-*r/ 78.0%

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

       2. *-rgt-identity 78.0%

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

   11. Simplified 78.0%

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

   12. Taylor expanded in x around 0 78.0%

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

       1. times-frac 78.0%

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

   14. Simplified 78.0%

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

   15. Taylor expanded in b around 0 91.7%

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

   if -7e3 < t < -4.2000000000000004e-30

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 86.7%

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

      4. associate-/l* 86.7%

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

      5. *-commutative 86.7%

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

      6. exp-to-pow 86.7%

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

      7. exp-diff 86.7%

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

      8. *-commutative 86.7%

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

      9. exp-to-pow 86.7%

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

      10. sub-neg 86.7%

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

      11. metadata-eval 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in y around 0 80.9%

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

      1. associate-/r* 67.6%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 80.9%

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

   if -4.2000000000000004e-30 < t < -5.20000000000000022e-141 or -2.9999999999999998e-183 < t < 2.79999999999999992e-298

   1. Initial program 97.1%

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

      1. associate-/l* 95.8%

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

      2. associate--l+ 95.8%

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

      3. exp-sum 82.5%

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

      4. associate-/l* 80.8%

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

      5. *-commutative 80.8%

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

      6. exp-to-pow 80.8%

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

      7. exp-diff 80.8%

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

      8. *-commutative 80.8%

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

      9. exp-to-pow 81.8%

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

      10. sub-neg 81.8%

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

      11. metadata-eval 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in t around 0 80.1%

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

   6. Taylor expanded in b around 0 70.6%

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

      1. *-commutative 70.6%

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

      2. times-frac 73.9%

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

   8. Simplified 73.9%

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

      1. associate-*l/ 83.6%

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

   10. Applied egg-rr 83.6%

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

   if -5.20000000000000022e-141 < t < -2.9999999999999998e-183

   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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 100.0%

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

      4. fma-define 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

   9. Applied egg-rr 100.0%

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

   10. Taylor expanded in b around inf 100.0%

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

       1. exp-neg 100.0%

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

       2. associate-*r/ 100.0%

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

       3. *-rgt-identity 100.0%

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

   12. Simplified 100.0%

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

   if 2.79999999999999992e-298 < t < 1.55e16

   1. Initial program 97.9%

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

      1. associate-/l* 94.2%

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

      2. associate--l+ 94.2%

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

      3. exp-sum 80.8%

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

      4. associate-/l* 79.3%

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

      5. *-commutative 79.3%

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

      6. exp-to-pow 79.3%

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

      7. exp-diff 77.8%

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

      8. *-commutative 77.8%

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

      9. exp-to-pow 79.2%

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

      10. sub-neg 79.2%

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

      11. metadata-eval 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/r* 66.6%

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

      2. exp-to-pow 67.9%

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

      3. sub-neg 67.9%

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

      4. metadata-eval 67.9%

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

   7. Simplified 67.9%

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

      1. unpow-prod-up 68.0%

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

      2. unpow-1 68.0%

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

   9. Applied egg-rr 68.0%

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

       1. associate-*r/ 68.0%

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

       2. *-rgt-identity 68.0%

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

   11. Simplified 68.0%

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

   12. Taylor expanded in x around 0 73.7%

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

       1. times-frac 69.2%

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

   14. Simplified 69.2%

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

       1. associate-*l/ 76.8%

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

   16. Applied egg-rr 76.8%

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

   17. Taylor expanded in t around 0 78.0%

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

       1. *-commutative 78.0%

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

       2. associate-/r* 78.0%

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

       3. rec-exp 78.0%

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

   19. Simplified 78.0%

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

   if 1.55e16 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 70.8%

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

      4. associate-/l* 70.8%

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

      5. *-commutative 70.8%

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

      6. exp-to-pow 70.8%

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

      7. exp-diff 47.9%

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

      8. *-commutative 47.9%

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

      9. exp-to-pow 47.9%

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

      10. sub-neg 47.9%

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

      11. metadata-eval 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in y around 0 58.5%

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

      1. associate-/r* 58.5%

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

      2. exp-to-pow 58.5%

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

      3. sub-neg 58.5%

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

      4. metadata-eval 58.5%

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

   7. Simplified 58.5%

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

      1. unpow-prod-up 58.5%

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

      2. unpow-1 58.5%

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

   9. Applied egg-rr 58.5%

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

       1. associate-*r/ 58.5%

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

       2. *-rgt-identity 58.5%

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

   11. Simplified 58.5%

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

   12. Taylor expanded in x around 0 48.0%

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

       1. times-frac 39.7%

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

   14. Simplified 39.7%

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

       1. associate-*l/ 58.5%

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

   16. Applied egg-rr 58.5%

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

   17. Taylor expanded in b around 0 71.3%

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

       1. associate-/l* 71.3%

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

   19. Simplified 71.3%

       \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{t}}{y}}}{a} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 8: 69.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8600:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x a) (/ (pow a t) y))))
   (if (<= b -7.2e+109)
     (/
      (* x (+ 1.0 (* b (+ (* b (+ 0.5 (* b -0.16666666666666666))) -1.0))))
      y)
     (if (<= b -1.6e+80)
       t_1
       (if (<= b -8600.0)
         (/ (/ x (exp b)) y)
         (if (<= b -4.4e-89)
           t_1
           (if (<= b -9.5e-114)
             (* x (/ 1.0 (* y a)))
             (if (<= b 2e-82) t_1 (/ x (* a (* y (exp b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) * (pow(a, t) / y);
	double tmp;
	if (b <= -7.2e+109) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -1.6e+80) {
		tmp = t_1;
	} else if (b <= -8600.0) {
		tmp = (x / exp(b)) / y;
	} else if (b <= -4.4e-89) {
		tmp = t_1;
	} else if (b <= -9.5e-114) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 2e-82) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) * ((a ** t) / y)
    if (b <= (-7.2d+109)) then
        tmp = (x * (1.0d0 + (b * ((b * (0.5d0 + (b * (-0.16666666666666666d0)))) + (-1.0d0))))) / y
    else if (b <= (-1.6d+80)) then
        tmp = t_1
    else if (b <= (-8600.0d0)) then
        tmp = (x / exp(b)) / y
    else if (b <= (-4.4d-89)) then
        tmp = t_1
    else if (b <= (-9.5d-114)) then
        tmp = x * (1.0d0 / (y * a))
    else if (b <= 2d-82) then
        tmp = t_1
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) * (Math.pow(a, t) / y);
	double tmp;
	if (b <= -7.2e+109) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -1.6e+80) {
		tmp = t_1;
	} else if (b <= -8600.0) {
		tmp = (x / Math.exp(b)) / y;
	} else if (b <= -4.4e-89) {
		tmp = t_1;
	} else if (b <= -9.5e-114) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 2e-82) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) * (math.pow(a, t) / y)
	tmp = 0
	if b <= -7.2e+109:
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y
	elif b <= -1.6e+80:
		tmp = t_1
	elif b <= -8600.0:
		tmp = (x / math.exp(b)) / y
	elif b <= -4.4e-89:
		tmp = t_1
	elif b <= -9.5e-114:
		tmp = x * (1.0 / (y * a))
	elif b <= 2e-82:
		tmp = t_1
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) * Float64((a ^ t) / y))
	tmp = 0.0
	if (b <= -7.2e+109)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))) + -1.0)))) / y);
	elseif (b <= -1.6e+80)
		tmp = t_1;
	elseif (b <= -8600.0)
		tmp = Float64(Float64(x / exp(b)) / y);
	elseif (b <= -4.4e-89)
		tmp = t_1;
	elseif (b <= -9.5e-114)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 2e-82)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) * ((a ^ t) / y);
	tmp = 0.0;
	if (b <= -7.2e+109)
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	elseif (b <= -1.6e+80)
		tmp = t_1;
	elseif (b <= -8600.0)
		tmp = (x / exp(b)) / y;
	elseif (b <= -4.4e-89)
		tmp = t_1;
	elseif (b <= -9.5e-114)
		tmp = x * (1.0 / (y * a));
	elseif (b <= 2e-82)
		tmp = t_1;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+109], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.6e+80], t$95$1, If[LessEqual[b, -8600.0], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -4.4e-89], t$95$1, If[LessEqual[b, -9.5e-114], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-82], t$95$1, N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.2e109

   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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 87.5%

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

      4. fma-define 87.5%

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

      5. sub-neg 87.5%

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

      6. metadata-eval 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in b around inf 81.3%

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

      1. neg-mul-1 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in b around 0 74.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in x around 0 87.9%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}}{y} \]

   11. Taylor expanded in x around 0 93.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}{y}} \]

   if -7.2e109 < b < -1.59999999999999995e80 or -8600 < b < -4.40000000000000024e-89 or -9.49999999999999958e-114 < b < 2e-82

   1. Initial program 97.5%

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

      1. associate-/l* 95.5%

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

      2. associate--l+ 95.5%

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

      3. exp-sum 84.7%

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

      4. associate-/l* 83.0%

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

      5. *-commutative 83.0%

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

      6. exp-to-pow 83.0%

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

      7. exp-diff 79.7%

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

      8. *-commutative 79.7%

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

      9. exp-to-pow 80.9%

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

      10. sub-neg 80.9%

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

      11. metadata-eval 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. associate-/r* 65.6%

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

      2. exp-to-pow 66.7%

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

      3. sub-neg 66.7%

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

      4. metadata-eval 66.7%

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

   7. Simplified 66.7%

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

      1. unpow-prod-up 66.8%

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

      2. unpow-1 66.8%

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

   9. Applied egg-rr 66.8%

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

       1. associate-*r/ 66.8%

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

       2. *-rgt-identity 66.8%

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

   11. Simplified 66.8%

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

   12. Taylor expanded in x around 0 64.0%

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

       1. times-frac 64.9%

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

   14. Simplified 64.9%

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

   15. Taylor expanded in b around 0 68.2%

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

   if -1.59999999999999995e80 < b < -8600

   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. *-commutative 100.0%

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

      2. associate-/l* 93.3%

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

      3. associate--l+ 93.3%

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

      4. fma-define 93.3%

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

      5. sub-neg 93.3%

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

      6. metadata-eval 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in b around inf 66.9%

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

      1. neg-mul-1 66.9%

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

   7. Simplified 66.9%

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

      1. associate-*r/ 73.8%

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

   9. Applied egg-rr 73.8%

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

   10. Taylor expanded in b around inf 73.8%

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

       1. exp-neg 73.8%

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

       2. associate-*r/ 73.8%

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

       3. *-rgt-identity 73.8%

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

   12. Simplified 73.8%

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

   if -4.40000000000000024e-89 < b < -9.49999999999999958e-114

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. exp-diff 75.0%

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

      8. *-commutative 75.0%

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

      9. exp-to-pow 75.0%

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

      10. sub-neg 75.0%

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

      11. metadata-eval 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in b around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. times-frac 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around 0 75.4%

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

       1. div-inv 75.4%

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

       2. *-commutative 75.4%

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

   11. Applied egg-rr 75.4%

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

   if 2e-82 < b

   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* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 73.9%

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

      4. associate-/l* 73.9%

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

      5. *-commutative 73.9%

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

      6. exp-to-pow 73.9%

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

      7. exp-diff 60.8%

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

      8. *-commutative 60.8%

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

      9. exp-to-pow 60.9%

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

      10. sub-neg 60.9%

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

      11. metadata-eval 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/r* 63.9%

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

      2. exp-to-pow 64.0%

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

      3. sub-neg 64.0%

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

      4. metadata-eval 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in t around 0 75.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq -8600:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -280:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-263}:\\ \;\;\;\;\frac{x - b \cdot \left(b \cdot \left(\frac{x}{b} - x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -280.0)
     t_1
     (if (<= b -1.15e-59)
       (/ (/ x a) y)
       (if (<= b -1.05e-167)
         (* (/ x y) (/ 1.0 a))
         (if (<= b -1.08e-263)
           (/ (- x (* b (* b (- (/ x b) (* x 0.5))))) y)
           (if (<= b 8.8e-39) (/ x (* y a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -280.0) {
		tmp = t_1;
	} else if (b <= -1.15e-59) {
		tmp = (x / a) / y;
	} else if (b <= -1.05e-167) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= -1.08e-263) {
		tmp = (x - (b * (b * ((x / b) - (x * 0.5))))) / y;
	} else if (b <= 8.8e-39) {
		tmp = x / (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 / exp(b)) / y
    if (b <= (-280.0d0)) then
        tmp = t_1
    else if (b <= (-1.15d-59)) then
        tmp = (x / a) / y
    else if (b <= (-1.05d-167)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= (-1.08d-263)) then
        tmp = (x - (b * (b * ((x / b) - (x * 0.5d0))))) / y
    else if (b <= 8.8d-39) then
        tmp = x / (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.exp(b)) / y;
	double tmp;
	if (b <= -280.0) {
		tmp = t_1;
	} else if (b <= -1.15e-59) {
		tmp = (x / a) / y;
	} else if (b <= -1.05e-167) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= -1.08e-263) {
		tmp = (x - (b * (b * ((x / b) - (x * 0.5))))) / y;
	} else if (b <= 8.8e-39) {
		tmp = x / (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -280.0:
		tmp = t_1
	elif b <= -1.15e-59:
		tmp = (x / a) / y
	elif b <= -1.05e-167:
		tmp = (x / y) * (1.0 / a)
	elif b <= -1.08e-263:
		tmp = (x - (b * (b * ((x / b) - (x * 0.5))))) / y
	elif b <= 8.8e-39:
		tmp = x / (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -280.0)
		tmp = t_1;
	elseif (b <= -1.15e-59)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= -1.05e-167)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= -1.08e-263)
		tmp = Float64(Float64(x - Float64(b * Float64(b * Float64(Float64(x / b) - Float64(x * 0.5))))) / y);
	elseif (b <= 8.8e-39)
		tmp = Float64(x / 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 / exp(b)) / y;
	tmp = 0.0;
	if (b <= -280.0)
		tmp = t_1;
	elseif (b <= -1.15e-59)
		tmp = (x / a) / y;
	elseif (b <= -1.05e-167)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= -1.08e-263)
		tmp = (x - (b * (b * ((x / b) - (x * 0.5))))) / y;
	elseif (b <= 8.8e-39)
		tmp = x / (y * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -280.0], t$95$1, If[LessEqual[b, -1.15e-59], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.05e-167], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.08e-263], N[(N[(x - N[(b * N[(b * N[(N[(x / b), $MachinePrecision] - N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 8.8e-39], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -280 or 8.80000000000000003e-39 < 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. *-commutative 100.0%

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

      2. associate-/l* 87.8%

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

      3. associate--l+ 87.8%

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

      4. fma-define 87.8%

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

      5. sub-neg 87.8%

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

      6. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf 68.7%

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

      1. neg-mul-1 68.7%

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

   7. Simplified 68.7%

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

      1. associate-*r/ 78.1%

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

   9. Applied egg-rr 78.1%

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

   10. Taylor expanded in b around inf 78.1%

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

       1. exp-neg 78.1%

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

       2. associate-*r/ 78.1%

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

       3. *-rgt-identity 78.1%

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

   12. Simplified 78.1%

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

   if -280 < b < -1.1499999999999999e-59

   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* 95.9%

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

      2. associate--l+ 95.9%

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

      3. exp-sum 86.8%

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

      4. associate-/l* 86.8%

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

      5. *-commutative 86.8%

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

      6. exp-to-pow 86.8%

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

      7. exp-diff 87.0%

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

      8. *-commutative 87.0%

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

      9. exp-to-pow 90.3%

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

      10. sub-neg 90.3%

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

      11. metadata-eval 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 74.4%

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

   6. Taylor expanded in b around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. times-frac 64.1%

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

   8. Simplified 64.1%

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

      1. associate-*l/ 81.9%

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

   10. Applied egg-rr 81.9%

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

   11. Taylor expanded in y around 0 64.8%

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

   if -1.1499999999999999e-59 < b < -1.05000000000000009e-167

   1. Initial program 99.1%

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

      1. associate-/l* 99.1%

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

      2. associate--l+ 99.1%

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

      3. exp-sum 84.8%

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

      4. associate-/l* 84.8%

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

      5. *-commutative 84.8%

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

      6. exp-to-pow 84.8%

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

      7. exp-diff 84.8%

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

      8. *-commutative 84.8%

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

      9. exp-to-pow 85.6%

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

      10. sub-neg 85.6%

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

      11. metadata-eval 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around 0 72.4%

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

   6. Taylor expanded in b around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. times-frac 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in y around 0 53.7%

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

   if -1.05000000000000009e-167 < b < -1.07999999999999998e-263

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-/l* 99.0%

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

      3. associate--l+ 99.0%

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

      4. fma-define 99.0%

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

      5. sub-neg 99.0%

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

      6. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in b around inf 8.2%

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

      1. neg-mul-1 8.2%

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

   7. Simplified 8.2%

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

   8. Taylor expanded in b around 0 8.2%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 8.2%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in b around 0 8.2%

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

       1. neg-mul-1 8.2%

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

       2. +-commutative 8.2%

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

       3. associate-*r* 8.2%

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

       4. neg-mul-1 8.2%

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

       5. distribute-rgt-out 8.2%

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

       6. *-commutative 8.2%

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

   12. Simplified 8.2%

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

   13. Taylor expanded in b around inf 38.7%

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

   if -1.07999999999999998e-263 < b < 8.80000000000000003e-39

   1. Initial program 97.9%

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

      1. associate-/l* 92.6%

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

      2. associate--l+ 92.6%

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

      3. exp-sum 86.2%

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

      4. associate-/l* 84.6%

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

      5. *-commutative 84.6%

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

      6. exp-to-pow 84.6%

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

      7. exp-diff 84.6%

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

      8. *-commutative 84.6%

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

      9. exp-to-pow 86.0%

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

      10. sub-neg 86.0%

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

      11. metadata-eval 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around 0 74.8%

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

   6. Taylor expanded in b around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. times-frac 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in y around 0 51.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -280:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-263}:\\ \;\;\;\;\frac{x - b \cdot \left(b \cdot \left(\frac{x}{b} - x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ \mathbf{if}\;x \leq 2.45 \cdot 10^{-194}:\\ \;\;\;\;\frac{\frac{x}{t\_1}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))))
   (if (<= x 2.45e-194) (/ (/ x t_1) a) (/ x (* a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double tmp;
	if (x <= 2.45e-194) {
		tmp = (x / t_1) / a;
	} else {
		tmp = x / (a * 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 = y * exp(b)
    if (x <= 2.45d-194) then
        tmp = (x / t_1) / a
    else
        tmp = x / (a * 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 = y * Math.exp(b);
	double tmp;
	if (x <= 2.45e-194) {
		tmp = (x / t_1) / a;
	} else {
		tmp = x / (a * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	tmp = 0
	if x <= 2.45e-194:
		tmp = (x / t_1) / a
	else:
		tmp = x / (a * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	tmp = 0.0
	if (x <= 2.45e-194)
		tmp = Float64(Float64(x / t_1) / a);
	else
		tmp = Float64(x / Float64(a * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	tmp = 0.0;
	if (x <= 2.45e-194)
		tmp = (x / t_1) / a;
	else
		tmp = x / (a * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 2.45e-194], N[(N[(x / t$95$1), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 2.45000000000000002e-194

   1. Initial program 98.4%

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

      1. associate-/l* 96.3%

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

      2. associate--l+ 96.3%

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

      3. exp-sum 78.1%

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

      4. associate-/l* 76.8%

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

      5. *-commutative 76.8%

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

      6. exp-to-pow 76.8%

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

      7. exp-diff 67.1%

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

      8. *-commutative 67.1%

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

      9. exp-to-pow 67.6%

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

      10. sub-neg 67.6%

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

      11. metadata-eval 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in y around 0 65.0%

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

      1. associate-/r* 63.0%

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

      2. exp-to-pow 63.6%

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

      3. sub-neg 63.6%

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

      4. metadata-eval 63.6%

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

   7. Simplified 63.6%

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

      1. unpow-prod-up 63.6%

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

      2. unpow-1 63.6%

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

   9. Applied egg-rr 63.6%

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

       1. associate-*r/ 63.6%

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

       2. *-rgt-identity 63.6%

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

   11. Simplified 63.6%

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

   12. Taylor expanded in x around 0 64.1%

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

       1. times-frac 63.4%

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

   14. Simplified 63.4%

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

       1. associate-*l/ 69.2%

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

   16. Applied egg-rr 69.2%

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

   17. Taylor expanded in t around 0 60.7%

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

   if 2.45000000000000002e-194 < x

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 78.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 78.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 79.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 79.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 79.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 72.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 72.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 72.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 72.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 72.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 66.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 59.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a \cdot \left(y \cdot e^{b}\right)} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* a (* y (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (a * (y * exp(b)));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (a * (y * exp(b)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (a * (y * Math.exp(b)));
}

Python

def code(x, y, z, t, a, b):
	return x / (a * (y * math.exp(b)))

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(a * Float64(y * exp(b))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (a * (y * exp(b)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 97.5%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 97.5%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 80.3%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 79.5%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 79.5%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 79.5%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 71.7%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 71.7%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 72.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 72.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 72.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 72.3%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 70.3%

   \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. associate-/r* 66.7%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

   2. exp-to-pow 67.3%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

   3. sub-neg 67.3%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

   4. metadata-eval 67.3%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

7. Simplified 67.3%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

8. Taylor expanded in t around 0 62.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
9. Add Preprocessing

Alternative 12: 40.0% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ t_2 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.1 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+245}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)) (t_2 (/ x (* y a))))
   (if (<= b -1.32e+128)
     (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y)
     (if (<= b -8.2e-17)
       (/ (- (/ x y) (* x (/ b y))) a)
       (if (<= b -5e-67)
         t_1
         (if (<= b -4e-163)
           (* (/ x y) (/ 1.0 a))
           (if (<= b 5e-209)
             t_2
             (if (<= b 8.1e+65)
               t_1
               (if (<= b 1.6e+245) t_2 (/ (/ x y) a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double t_2 = x / (y * a);
	double tmp;
	if (b <= -1.32e+128) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= -8.2e-17) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -5e-67) {
		tmp = t_1;
	} else if (b <= -4e-163) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 5e-209) {
		tmp = t_2;
	} else if (b <= 8.1e+65) {
		tmp = t_1;
	} else if (b <= 1.6e+245) {
		tmp = t_2;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / a) / y
    t_2 = x / (y * a)
    if (b <= (-1.32d+128)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else if (b <= (-8.2d-17)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= (-5d-67)) then
        tmp = t_1
    else if (b <= (-4d-163)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 5d-209) then
        tmp = t_2
    else if (b <= 8.1d+65) then
        tmp = t_1
    else if (b <= 1.6d+245) then
        tmp = t_2
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double t_2 = x / (y * a);
	double tmp;
	if (b <= -1.32e+128) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= -8.2e-17) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -5e-67) {
		tmp = t_1;
	} else if (b <= -4e-163) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 5e-209) {
		tmp = t_2;
	} else if (b <= 8.1e+65) {
		tmp = t_1;
	} else if (b <= 1.6e+245) {
		tmp = t_2;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	t_2 = x / (y * a)
	tmp = 0
	if b <= -1.32e+128:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	elif b <= -8.2e-17:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= -5e-67:
		tmp = t_1
	elif b <= -4e-163:
		tmp = (x / y) * (1.0 / a)
	elif b <= 5e-209:
		tmp = t_2
	elif b <= 8.1e+65:
		tmp = t_1
	elif b <= 1.6e+245:
		tmp = t_2
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	t_2 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -1.32e+128)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	elseif (b <= -8.2e-17)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= -5e-67)
		tmp = t_1;
	elseif (b <= -4e-163)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 5e-209)
		tmp = t_2;
	elseif (b <= 8.1e+65)
		tmp = t_1;
	elseif (b <= 1.6e+245)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	t_2 = x / (y * a);
	tmp = 0.0;
	if (b <= -1.32e+128)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	elseif (b <= -8.2e-17)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= -5e-67)
		tmp = t_1;
	elseif (b <= -4e-163)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 5e-209)
		tmp = t_2;
	elseif (b <= 8.1e+65)
		tmp = t_1;
	elseif (b <= 1.6e+245)
		tmp = t_2;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.32e+128], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -8.2e-17], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -5e-67], t$95$1, If[LessEqual[b, -4e-163], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e-209], t$95$2, If[LessEqual[b, 8.1e+65], t$95$1, If[LessEqual[b, 1.6e+245], t$95$2, N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.31999999999999991e128

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 86.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 86.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 86.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 79.1%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 79.1%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 79.1%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 78.0%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 86.4%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in b around 0 77.4%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(-1 \cdot x + 0.5 \cdot \left(b \cdot x\right)\right)}}{y} \]
   11. Step-by-step derivation

       1. neg-mul-1 77.4%

          \[\leadsto \frac{x + b \cdot \left(\color{blue}{\left(-x\right)} + 0.5 \cdot \left(b \cdot x\right)\right)}{y} \]

       2. +-commutative 77.4%

          \[\leadsto \frac{x + b \cdot \color{blue}{\left(0.5 \cdot \left(b \cdot x\right) + \left(-x\right)\right)}}{y} \]

       3. associate-*r* 77.4%

          \[\leadsto \frac{x + b \cdot \left(\color{blue}{\left(0.5 \cdot b\right) \cdot x} + \left(-x\right)\right)}{y} \]

       4. neg-mul-1 77.4%

          \[\leadsto \frac{x + b \cdot \left(\left(0.5 \cdot b\right) \cdot x + \color{blue}{-1 \cdot x}\right)}{y} \]

       5. distribute-rgt-out 77.4%

          \[\leadsto \frac{x + b \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot b + -1\right)\right)}}{y} \]

       6. *-commutative 77.4%

          \[\leadsto \frac{x + b \cdot \left(x \cdot \left(\color{blue}{b \cdot 0.5} + -1\right)\right)}{y} \]

   12. Simplified 77.4%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   13. Taylor expanded in x around 0 88.6%

       \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(0.5 \cdot b - 1\right)\right)}{y}} \]

   if -1.31999999999999991e128 < b < -8.2000000000000001e-17

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 63.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 63.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 63.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 63.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 63.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 63.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.0%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 61.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 61.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 61.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 61.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 61.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 61.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y}}{e^{b}} \]

      2. unpow-1 61.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y}}{e^{b}} \]

   9. Applied egg-rr 61.5%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y}}{e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 61.5%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y}}{e^{b}} \]

       2. *-rgt-identity 61.5%

          \[\leadsto x \cdot \frac{\frac{\frac{\color{blue}{{a}^{t}}}{a}}{y}}{e^{b}} \]

   11. Simplified 61.5%

       \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t}}{a}}}{y}}{e^{b}} \]

   12. Taylor expanded in x around 0 64.3%

       \[\leadsto \color{blue}{\frac{x \cdot {a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. times-frac 55.9%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{a}^{t}}{y \cdot e^{b}}} \]

   14. Simplified 55.9%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{a}^{t}}{y \cdot e^{b}}} \]
   15. Step-by-step derivation

       1. associate-*l/ 64.3%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{t}}{y \cdot e^{b}}}{a}} \]

   16. Applied egg-rr 64.3%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{t}}{y \cdot e^{b}}}{a}} \]

   17. Taylor expanded in t around 0 64.6%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{y \cdot e^{b}}}}{a} \]
   18. Step-by-step derivation

       1. *-commutative 64.6%

          \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot y}}}{a} \]

       2. associate-/r* 64.7%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{e^{b}}}{y}}}{a} \]

       3. rec-exp 64.7%

          \[\leadsto \frac{x \cdot \frac{\color{blue}{e^{-b}}}{y}}{a} \]

   19. Simplified 64.7%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-b}}{y}}}{a} \]

   20. Taylor expanded in b around 0 27.5%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}}}{a} \]
   21. Step-by-step derivation

       1. +-commutative 27.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}}}{a} \]

       2. mul-1-neg 27.5%

          \[\leadsto \frac{\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}}{a} \]

       3. unsub-neg 27.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}}}{a} \]

       4. *-commutative 27.5%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}}{a} \]

       5. associate-/l* 32.8%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{x \cdot \frac{b}{y}}}{a} \]

   22. Simplified 32.8%

       \[\leadsto \frac{\color{blue}{\frac{x}{y} - x \cdot \frac{b}{y}}}{a} \]

   if -8.2000000000000001e-17 < b < -4.9999999999999999e-67 or 5.0000000000000005e-209 < b < 8.1000000000000001e65

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 95.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 95.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 79.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 77.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 77.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 77.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 72.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 72.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 73.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 73.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 73.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 60.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 59.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 59.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 59.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   10. Applied egg-rr 72.7%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   11. Taylor expanded in y around 0 42.2%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -4.9999999999999999e-67 < b < -3.99999999999999969e-163

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 82.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 82.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 83.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 83.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 83.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 73.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 72.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 56.7%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]

   if -3.99999999999999969e-163 < b < 5.0000000000000005e-209 or 8.1000000000000001e65 < b < 1.60000000000000012e245

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 95.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 95.8%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 82.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.1%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.1%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.1%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 78.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 78.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 79.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 79.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 79.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 57.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 57.9%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 60.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 38.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 1.60000000000000012e245 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 31.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 31.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 31.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 27.2%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]
   10. Step-by-step derivation

       1. un-div-inv 27.2%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   11. Applied egg-rr 27.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.1 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+245}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{+165}:\\ \;\;\;\;\frac{x + b \cdot \left(x \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (/ (/ x a) y)))
   (if (<= b -1.72e+165)
     (/ (+ x (* b (* x (* b 0.5)))) y)
     (if (<= b -1.26e-65)
       t_2
       (if (<= b -2e-161)
         (* (/ x y) (/ 1.0 a))
         (if (<= b 7e-206)
           t_1
           (if (<= b 2e+123) t_2 (if (<= b 1.55e+245) t_1 (/ (/ x y) a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -1.72e+165) {
		tmp = (x + (b * (x * (b * 0.5)))) / y;
	} else if (b <= -1.26e-65) {
		tmp = t_2;
	} else if (b <= -2e-161) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 7e-206) {
		tmp = t_1;
	} else if (b <= 2e+123) {
		tmp = t_2;
	} else if (b <= 1.55e+245) {
		tmp = t_1;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = (x / a) / y
    if (b <= (-1.72d+165)) then
        tmp = (x + (b * (x * (b * 0.5d0)))) / y
    else if (b <= (-1.26d-65)) then
        tmp = t_2
    else if (b <= (-2d-161)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 7d-206) then
        tmp = t_1
    else if (b <= 2d+123) then
        tmp = t_2
    else if (b <= 1.55d+245) then
        tmp = t_1
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -1.72e+165) {
		tmp = (x + (b * (x * (b * 0.5)))) / y;
	} else if (b <= -1.26e-65) {
		tmp = t_2;
	} else if (b <= -2e-161) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 7e-206) {
		tmp = t_1;
	} else if (b <= 2e+123) {
		tmp = t_2;
	} else if (b <= 1.55e+245) {
		tmp = t_1;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = (x / a) / y
	tmp = 0
	if b <= -1.72e+165:
		tmp = (x + (b * (x * (b * 0.5)))) / y
	elif b <= -1.26e-65:
		tmp = t_2
	elif b <= -2e-161:
		tmp = (x / y) * (1.0 / a)
	elif b <= 7e-206:
		tmp = t_1
	elif b <= 2e+123:
		tmp = t_2
	elif b <= 1.55e+245:
		tmp = t_1
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.72e+165)
		tmp = Float64(Float64(x + Float64(b * Float64(x * Float64(b * 0.5)))) / y);
	elseif (b <= -1.26e-65)
		tmp = t_2;
	elseif (b <= -2e-161)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 7e-206)
		tmp = t_1;
	elseif (b <= 2e+123)
		tmp = t_2;
	elseif (b <= 1.55e+245)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = (x / a) / y;
	tmp = 0.0;
	if (b <= -1.72e+165)
		tmp = (x + (b * (x * (b * 0.5)))) / y;
	elseif (b <= -1.26e-65)
		tmp = t_2;
	elseif (b <= -2e-161)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 7e-206)
		tmp = t_1;
	elseif (b <= 2e+123)
		tmp = t_2;
	elseif (b <= 1.55e+245)
		tmp = t_1;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.72e+165], N[(N[(x + N[(b * N[(x * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.26e-65], t$95$2, If[LessEqual[b, -2e-161], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-206], t$95$1, If[LessEqual[b, 2e+123], t$95$2, If[LessEqual[b, 1.55e+245], t$95$1, N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.72e165

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 88.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.2%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 82.4%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 82.4%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 82.4%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 85.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 88.6%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in b around 0 85.7%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(-1 \cdot x + 0.5 \cdot \left(b \cdot x\right)\right)}}{y} \]
   11. Step-by-step derivation

       1. neg-mul-1 85.7%

          \[\leadsto \frac{x + b \cdot \left(\color{blue}{\left(-x\right)} + 0.5 \cdot \left(b \cdot x\right)\right)}{y} \]

       2. +-commutative 85.7%

          \[\leadsto \frac{x + b \cdot \color{blue}{\left(0.5 \cdot \left(b \cdot x\right) + \left(-x\right)\right)}}{y} \]

       3. associate-*r* 85.7%

          \[\leadsto \frac{x + b \cdot \left(\color{blue}{\left(0.5 \cdot b\right) \cdot x} + \left(-x\right)\right)}{y} \]

       4. neg-mul-1 85.7%

          \[\leadsto \frac{x + b \cdot \left(\left(0.5 \cdot b\right) \cdot x + \color{blue}{-1 \cdot x}\right)}{y} \]

       5. distribute-rgt-out 85.7%

          \[\leadsto \frac{x + b \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot b + -1\right)\right)}}{y} \]

       6. *-commutative 85.7%

          \[\leadsto \frac{x + b \cdot \left(x \cdot \left(\color{blue}{b \cdot 0.5} + -1\right)\right)}{y} \]

   12. Simplified 85.7%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot 0.5 + -1\right)\right)}}{y} \]

   13. Taylor expanded in b around inf 85.7%

       \[\leadsto \frac{x + b \cdot \color{blue}{\left(0.5 \cdot \left(b \cdot x\right)\right)}}{y} \]
   14. Step-by-step derivation

       1. associate-*r* 85.7%

          \[\leadsto \frac{x + b \cdot \color{blue}{\left(\left(0.5 \cdot b\right) \cdot x\right)}}{y} \]

       2. *-commutative 85.7%

          \[\leadsto \frac{x + b \cdot \left(\color{blue}{\left(b \cdot 0.5\right)} \cdot x\right)}{y} \]

       3. *-commutative 85.7%

          \[\leadsto \frac{x + b \cdot \color{blue}{\left(x \cdot \left(b \cdot 0.5\right)\right)}}{y} \]

   15. Simplified 85.7%

       \[\leadsto \frac{x + b \cdot \color{blue}{\left(x \cdot \left(b \cdot 0.5\right)\right)}}{y} \]

   if -1.72e165 < b < -1.26e-65 or 6.99999999999999979e-206 < b < 1.99999999999999996e123

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 77.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 77.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 77.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 68.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 68.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 69.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 69.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 69.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 63.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 63.1%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 62.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 73.6%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   10. Applied egg-rr 73.6%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   11. Taylor expanded in y around 0 37.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -1.26e-65 < b < -2.00000000000000006e-161

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 82.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 82.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 83.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 83.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 83.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 73.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 72.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 56.7%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]

   if -2.00000000000000006e-161 < b < 6.99999999999999979e-206 or 1.99999999999999996e123 < b < 1.5499999999999999e245

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 95.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 95.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 59.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 63.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 63.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 41.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 1.5499999999999999e245 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 31.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 31.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 31.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 27.2%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]
   10. Step-by-step derivation

       1. un-div-inv 27.2%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   11. Applied egg-rr 27.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+165}:\\ \;\;\;\;\frac{x + b \cdot \left(x \cdot \left(b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+245}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.3% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} - b \cdot \left(\frac{1}{y} + b \cdot \left(0.5 \cdot \frac{-1}{y} - -0.16666666666666666 \cdot \frac{b}{y}\right)\right)\right)}{a}\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-266}:\\ \;\;\;\;\frac{x + b \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{0.5}{b} - 0.16666666666666666\right)\right)\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e-187)
   (/
    (*
     x
     (-
      (/ 1.0 y)
      (*
       b
       (+
        (/ 1.0 y)
        (* b (- (* 0.5 (/ -1.0 y)) (* -0.16666666666666666 (/ b y))))))))
    a)
   (if (<= b -1.55e-266)
     (/
      (+ x (* b (- (* b (* b (* x (- (/ 0.5 b) 0.16666666666666666)))) x)))
      y)
     (/ x (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e-187) {
		tmp = (x * ((1.0 / y) - (b * ((1.0 / y) + (b * ((0.5 * (-1.0 / y)) - (-0.16666666666666666 * (b / y)))))))) / a;
	} else if (b <= -1.55e-266) {
		tmp = (x + (b * ((b * (b * (x * ((0.5 / b) - 0.16666666666666666)))) - x))) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.1d-187)) then
        tmp = (x * ((1.0d0 / y) - (b * ((1.0d0 / y) + (b * ((0.5d0 * ((-1.0d0) / y)) - ((-0.16666666666666666d0) * (b / y)))))))) / a
    else if (b <= (-1.55d-266)) then
        tmp = (x + (b * ((b * (b * (x * ((0.5d0 / b) - 0.16666666666666666d0)))) - x))) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e-187) {
		tmp = (x * ((1.0 / y) - (b * ((1.0 / y) + (b * ((0.5 * (-1.0 / y)) - (-0.16666666666666666 * (b / y)))))))) / a;
	} else if (b <= -1.55e-266) {
		tmp = (x + (b * ((b * (b * (x * ((0.5 / b) - 0.16666666666666666)))) - x))) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1e-187:
		tmp = (x * ((1.0 / y) - (b * ((1.0 / y) + (b * ((0.5 * (-1.0 / y)) - (-0.16666666666666666 * (b / y)))))))) / a
	elif b <= -1.55e-266:
		tmp = (x + (b * ((b * (b * (x * ((0.5 / b) - 0.16666666666666666)))) - x))) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e-187)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / y) - Float64(b * Float64(Float64(1.0 / y) + Float64(b * Float64(Float64(0.5 * Float64(-1.0 / y)) - Float64(-0.16666666666666666 * Float64(b / y)))))))) / a);
	elseif (b <= -1.55e-266)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(b * Float64(b * Float64(x * Float64(Float64(0.5 / b) - 0.16666666666666666)))) - x))) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e-187)
		tmp = (x * ((1.0 / y) - (b * ((1.0 / y) + (b * ((0.5 * (-1.0 / y)) - (-0.16666666666666666 * (b / y)))))))) / a;
	elseif (b <= -1.55e-266)
		tmp = (x + (b * ((b * (b * (x * ((0.5 / b) - 0.16666666666666666)))) - x))) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e-187], N[(N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b * N[(N[(1.0 / y), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(-1.0 / y), $MachinePrecision]), $MachinePrecision] - N[(-0.16666666666666666 * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -1.55e-266], N[(N[(x + N[(b * N[(N[(b * N[(b * N[(x * N[(N[(0.5 / b), $MachinePrecision] - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.10000000000000004e-187

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 71.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 71.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 71.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 68.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 68.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 68.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 68.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 68.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y}}{e^{b}} \]

      2. unpow-1 68.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y}}{e^{b}} \]

   9. Applied egg-rr 68.8%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y}}{e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 68.8%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y}}{e^{b}} \]

       2. *-rgt-identity 68.8%

          \[\leadsto x \cdot \frac{\frac{\frac{\color{blue}{{a}^{t}}}{a}}{y}}{e^{b}} \]

   11. Simplified 68.8%

       \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t}}{a}}}{y}}{e^{b}} \]

   12. Taylor expanded in x around 0 71.4%

       \[\leadsto \color{blue}{\frac{x \cdot {a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. times-frac 66.1%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{a}^{t}}{y \cdot e^{b}}} \]

   14. Simplified 66.1%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{a}^{t}}{y \cdot e^{b}}} \]
   15. Step-by-step derivation

       1. associate-*l/ 73.3%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{t}}{y \cdot e^{b}}}{a}} \]

   16. Applied egg-rr 73.3%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{t}}{y \cdot e^{b}}}{a}} \]

   17. Taylor expanded in t around 0 71.9%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{y \cdot e^{b}}}}{a} \]
   18. Step-by-step derivation

       1. *-commutative 71.9%

          \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot y}}}{a} \]

       2. associate-/r* 71.9%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{\frac{1}{e^{b}}}{y}}}{a} \]

       3. rec-exp 71.9%

          \[\leadsto \frac{x \cdot \frac{\color{blue}{e^{-b}}}{y}}{a} \]

   19. Simplified 71.9%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-b}}{y}}}{a} \]

   20. Taylor expanded in b around 0 63.4%

       \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) - \frac{1}{y}\right) + \frac{1}{y}\right)}}{a} \]

   if -1.10000000000000004e-187 < b < -1.54999999999999998e-266

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 99.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 99.1%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 99.1%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 99.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 99.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 8.9%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 8.9%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 8.9%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 8.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 8.9%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in b around inf 44.3%

       \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \color{blue}{\left(b \cdot \left(-0.16666666666666666 \cdot x + 0.5 \cdot \frac{x}{b}\right)\right)}\right)}{y} \]

   11. Taylor expanded in x around -inf 44.3%

       \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(x \cdot \left(0.16666666666666666 - 0.5 \cdot \frac{1}{b}\right)\right)\right)\right)}\right)}{y} \]
   12. Step-by-step derivation

       1. associate-*r* 44.3%

          \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot \left(x \cdot \left(0.16666666666666666 - 0.5 \cdot \frac{1}{b}\right)\right)\right)}\right)}{y} \]

       2. neg-mul-1 44.3%

          \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(\color{blue}{\left(-b\right)} \cdot \left(x \cdot \left(0.16666666666666666 - 0.5 \cdot \frac{1}{b}\right)\right)\right)\right)}{y} \]

       3. associate-*r/ 44.3%

          \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(\left(-b\right) \cdot \left(x \cdot \left(0.16666666666666666 - \color{blue}{\frac{0.5 \cdot 1}{b}}\right)\right)\right)\right)}{y} \]

       4. metadata-eval 44.3%

          \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(\left(-b\right) \cdot \left(x \cdot \left(0.16666666666666666 - \frac{\color{blue}{0.5}}{b}\right)\right)\right)\right)}{y} \]

   13. Simplified 44.3%

       \[\leadsto \frac{x + b \cdot \left(-1 \cdot x + b \cdot \color{blue}{\left(\left(-b\right) \cdot \left(x \cdot \left(0.16666666666666666 - \frac{0.5}{b}\right)\right)\right)}\right)}{y} \]

   if -1.54999999999999998e-266 < b

   1. Initial program 98.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 79.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 71.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 71.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 72.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 72.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 72.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 70.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 54.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 54.8%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 53.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 36.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} - b \cdot \left(\frac{1}{y} + b \cdot \left(0.5 \cdot \frac{-1}{y} - -0.16666666666666666 \cdot \frac{b}{y}\right)\right)\right)}{a}\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-266}:\\ \;\;\;\;\frac{x + b \cdot \left(b \cdot \left(b \cdot \left(x \cdot \left(\frac{0.5}{b} - 0.16666666666666666\right)\right)\right) - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.2% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e+109)
   (/ (* x (+ 1.0 (* b (+ (* b (+ 0.5 (* b -0.16666666666666666))) -1.0)))) y)
   (if (<= b -3.9e-38)
     (* (/ x a) (/ 1.0 y))
     (if (<= b -2.5e-162) (* (/ x y) (/ 1.0 a)) (/ x (* y a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+109) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -3.9e-38) {
		tmp = (x / a) * (1.0 / y);
	} else if (b <= -2.5e-162) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7d+109)) then
        tmp = (x * (1.0d0 + (b * ((b * (0.5d0 + (b * (-0.16666666666666666d0)))) + (-1.0d0))))) / y
    else if (b <= (-3.9d-38)) then
        tmp = (x / a) * (1.0d0 / y)
    else if (b <= (-2.5d-162)) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+109) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else if (b <= -3.9e-38) {
		tmp = (x / a) * (1.0 / y);
	} else if (b <= -2.5e-162) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+109:
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y
	elif b <= -3.9e-38:
		tmp = (x / a) * (1.0 / y)
	elif b <= -2.5e-162:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+109)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))) + -1.0)))) / y);
	elseif (b <= -3.9e-38)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	elseif (b <= -2.5e-162)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e+109)
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	elseif (b <= -3.9e-38)
		tmp = (x / a) * (1.0 / y);
	elseif (b <= -2.5e-162)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+109], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.9e-38], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-162], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.99999999999999966e109

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 87.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 81.3%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 81.3%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 81.3%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 74.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in x around 0 87.9%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}}{y} \]

   11. Taylor expanded in x around 0 93.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}{y}} \]

   if -6.99999999999999966e109 < b < -3.8999999999999999e-38

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 79.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 62.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 62.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 63.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 63.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 63.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 59.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 70.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 70.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 70.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 78.3%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   10. Applied egg-rr 78.3%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   11. Taylor expanded in y around 0 38.2%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
   12. Step-by-step derivation

       1. div-inv 38.3%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

   13. Applied egg-rr 38.3%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

   if -3.8999999999999999e-38 < b < -2.50000000000000007e-162

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 70.6%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 70.6%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 65.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 65.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 49.1%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]

   if -2.50000000000000007e-162 < b

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 73.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 73.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 74.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 74.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 74.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 54.6%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 56.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 34.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.5% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+165}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.72e+165)
   (/ (- x (* x b)) y)
   (if (<= b -6e-59)
     (/ (/ x a) y)
     (if (<= b -1.9e-167) (* (/ x y) (/ 1.0 a)) (/ x (* y a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.72e+165) {
		tmp = (x - (x * b)) / y;
	} else if (b <= -6e-59) {
		tmp = (x / a) / y;
	} else if (b <= -1.9e-167) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.72d+165)) then
        tmp = (x - (x * b)) / y
    else if (b <= (-6d-59)) then
        tmp = (x / a) / y
    else if (b <= (-1.9d-167)) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.72e+165) {
		tmp = (x - (x * b)) / y;
	} else if (b <= -6e-59) {
		tmp = (x / a) / y;
	} else if (b <= -1.9e-167) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.72e+165:
		tmp = (x - (x * b)) / y
	elif b <= -6e-59:
		tmp = (x / a) / y
	elif b <= -1.9e-167:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.72e+165)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	elseif (b <= -6e-59)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= -1.9e-167)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.72e+165)
		tmp = (x - (x * b)) / y;
	elseif (b <= -6e-59)
		tmp = (x / a) / y;
	elseif (b <= -1.9e-167)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.72e+165], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -6e-59], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.9e-167], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.72e165

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 88.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.2%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 82.4%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 82.4%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 82.4%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 85.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 88.6%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in b around 0 60.4%

       \[\leadsto \frac{x + \color{blue}{-1 \cdot \left(b \cdot x\right)}}{y} \]
   11. Step-by-step derivation

       1. mul-1-neg 60.4%

          \[\leadsto \frac{x + \color{blue}{\left(-b \cdot x\right)}}{y} \]

       2. distribute-rgt-neg-out 60.4%

          \[\leadsto \frac{x + \color{blue}{b \cdot \left(-x\right)}}{y} \]

   12. Simplified 60.4%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(-x\right)}}{y} \]

   if -1.72e165 < b < -6.0000000000000002e-59

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 69.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 69.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 69.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 69.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 69.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 70.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 70.5%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 68.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 79.7%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   10. Applied egg-rr 79.7%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   11. Taylor expanded in y around 0 39.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -6.0000000000000002e-59 < b < -1.89999999999999984e-167

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 84.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 84.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 84.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 84.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 84.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 85.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 85.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 85.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 72.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 72.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 72.4%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 72.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 53.7%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]

   if -1.89999999999999984e-167 < b

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 73.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 73.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 73.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 73.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 73.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 54.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 56.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 33.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+165}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.7% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.2e-23) (* x (/ 1.0 (* y a))) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e-23) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.2d-23)) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e-23) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.2e-23:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.2e-23)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.2e-23)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.2e-23], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.2000000000000004e-23

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 70.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 70.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 70.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 59.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 58.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 51.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 37.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. div-inv 38.4%

          \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

       2. *-commutative 38.4%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot a}} \]

   11. Applied egg-rr 38.4%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   if -9.2000000000000004e-23 < t

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 79.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 72.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 72.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 72.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 72.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 72.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 72.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 56.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 60.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 33.3%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 31.7% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e-24) (* x (/ 1.0 (* y a))) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-24) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.2d-24)) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-24) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e-24:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e-24)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e-24)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e-24], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000002e-24

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 70.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 70.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 70.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 70.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 59.3%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 58.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 51.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 37.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. div-inv 38.4%

          \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]

       2. *-commutative 38.4%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot a}} \]

   11. Applied egg-rr 38.4%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   if -2.20000000000000002e-24 < t

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 79.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 72.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 72.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 72.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 72.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 72.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 72.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 56.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 60.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 33.3%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]
   10. Step-by-step derivation

       1. un-div-inv 33.2%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   11. Applied egg-rr 33.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 31.6% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{-167}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.9e-167) (/ (/ x a) y) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.9e-167) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.9d-167) then
        tmp = (x / a) / y
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.9e-167) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.9e-167:
		tmp = (x / a) / y
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.9e-167)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.9e-167)
		tmp = (x / a) / y;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.9e-167], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.89999999999999984e-167

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.2%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.2%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.2%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 72.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 60.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 60.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 60.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 67.5%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   10. Applied egg-rr 67.5%

       \[\leadsto \color{blue}{\frac{x \cdot \frac{{z}^{y}}{a}}{y}} \]

   11. Taylor expanded in y around 0 39.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 1.89999999999999984e-167 < t

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 74.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 74.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 74.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 74.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 61.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 61.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 61.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 61.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 61.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 61.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 50.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

      2. times-frac 53.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   8. Simplified 53.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

   9. Taylor expanded in y around 0 26.6%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{a}} \]
   10. Step-by-step derivation

       1. un-div-inv 26.6%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   11. Applied egg-rr 26.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 31.0% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 97.5%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 97.5%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 80.3%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 79.5%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 79.5%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 79.5%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 71.7%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 71.7%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 72.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 72.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 72.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 72.3%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 68.8%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]

6. Taylor expanded in b around 0 56.9%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
7. Step-by-step derivation

   1. *-commutative 56.9%

      \[\leadsto \frac{x \cdot {z}^{y}}{\color{blue}{y \cdot a}} \]

   2. times-frac 57.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

8. Simplified 57.7%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{{z}^{y}}{a}} \]

9. Taylor expanded in y around 0 33.0%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 33.0%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Alternative 21: 16.0% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 98.8%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 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. associate--l+ 89.2%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 89.2%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 89.2%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 89.2%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 89.2%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 45.2%

   \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
6. Step-by-step derivation

   1. neg-mul-1 45.2%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

7. Simplified 45.2%

   \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

8. Taylor expanded in b around 0 16.5%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer target: 71.6% 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 2024107 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))