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

Percentage Accurate: 98.3% → 98.3%

Time: 32.7s

Alternatives: 29

Speedup: 1.0×

• 46.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

3. Final simplification 97.8%

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

Alternative 2: 73.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ t_2 := \frac{x}{y} \cdot e^{y \cdot \log z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -115:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow a (+ t -1.0)) y) (exp b))))
        (t_2 (* (/ x y) (exp (* y (log z))))))
   (if (<= y -9.5e+171)
     t_2
     (if (<= y -4.1e+80)
       t_1
       (if (<= y -115.0)
         (/ (* x (pow z y)) (* y a))
         (if (<= y 1.65e-168)
           t_1
           (if (<= y 3.2e-117)
             (/ (* x (pow a t)) (* y a))
             (if (<= y 2.5e-28) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(a, (t + -1.0)) / y) / exp(b));
	double t_2 = (x / y) * exp((y * log(z)));
	double tmp;
	if (y <= -9.5e+171) {
		tmp = t_2;
	} else if (y <= -4.1e+80) {
		tmp = t_1;
	} else if (y <= -115.0) {
		tmp = (x * pow(z, y)) / (y * a);
	} else if (y <= 1.65e-168) {
		tmp = t_1;
	} else if (y <= 3.2e-117) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 2.5e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((a ** (t + (-1.0d0))) / y) / exp(b))
    t_2 = (x / y) * exp((y * log(z)))
    if (y <= (-9.5d+171)) then
        tmp = t_2
    else if (y <= (-4.1d+80)) then
        tmp = t_1
    else if (y <= (-115.0d0)) then
        tmp = (x * (z ** y)) / (y * a)
    else if (y <= 1.65d-168) then
        tmp = t_1
    else if (y <= 3.2d-117) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 2.5d-28) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((Math.pow(a, (t + -1.0)) / y) / Math.exp(b));
	double t_2 = (x / y) * Math.exp((y * Math.log(z)));
	double tmp;
	if (y <= -9.5e+171) {
		tmp = t_2;
	} else if (y <= -4.1e+80) {
		tmp = t_1;
	} else if (y <= -115.0) {
		tmp = (x * Math.pow(z, y)) / (y * a);
	} else if (y <= 1.65e-168) {
		tmp = t_1;
	} else if (y <= 3.2e-117) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 2.5e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(a, (t + -1.0)) / y) / math.exp(b))
	t_2 = (x / y) * math.exp((y * math.log(z)))
	tmp = 0
	if y <= -9.5e+171:
		tmp = t_2
	elif y <= -4.1e+80:
		tmp = t_1
	elif y <= -115.0:
		tmp = (x * math.pow(z, y)) / (y * a)
	elif y <= 1.65e-168:
		tmp = t_1
	elif y <= 3.2e-117:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 2.5e-28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / y) / exp(b)))
	t_2 = Float64(Float64(x / y) * exp(Float64(y * log(z))))
	tmp = 0.0
	if (y <= -9.5e+171)
		tmp = t_2;
	elseif (y <= -4.1e+80)
		tmp = t_1;
	elseif (y <= -115.0)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(y * a));
	elseif (y <= 1.65e-168)
		tmp = t_1;
	elseif (y <= 3.2e-117)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 2.5e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((a ^ (t + -1.0)) / y) / exp(b));
	t_2 = (x / y) * exp((y * log(z)));
	tmp = 0.0;
	if (y <= -9.5e+171)
		tmp = t_2;
	elseif (y <= -4.1e+80)
		tmp = t_1;
	elseif (y <= -115.0)
		tmp = (x * (z ^ y)) / (y * a);
	elseif (y <= 1.65e-168)
		tmp = t_1;
	elseif (y <= 3.2e-117)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 2.5e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+171], t$95$2, If[LessEqual[y, -4.1e+80], t$95$1, If[LessEqual[y, -115.0], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-168], t$95$1, If[LessEqual[y, 3.2e-117], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-28], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.49999999999999924e171 or 2.5000000000000001e-28 < 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* 94.1%

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

      3. associate--l+ 94.1%

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

      4. fma-define 94.1%

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

      5. sub-neg 94.1%

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

      6. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 82.4%

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

   if -9.49999999999999924e171 < y < -4.10000000000000001e80 or -115 < y < 1.6500000000000001e-168 or 3.19999999999999995e-117 < y < 2.5000000000000001e-28

   1. Initial program 95.8%

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

      1. associate-/l* 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 93.4%

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

      4. associate-/l* 92.7%

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

      5. *-commutative 92.7%

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

      6. exp-to-pow 92.7%

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

      7. exp-diff 82.1%

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

      8. *-commutative 82.1%

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

      9. exp-to-pow 83.3%

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

      10. sub-neg 83.3%

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

      11. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. associate-/r* 82.1%

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

      2. exp-to-pow 83.3%

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

      3. sub-neg 83.3%

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

      4. metadata-eval 83.3%

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

   7. Simplified 83.3%

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

   if -4.10000000000000001e80 < y < -115

   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 80.0%

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

   6. Taylor expanded in b around 0 90.2%

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

      1. *-commutative 90.2%

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

   8. Simplified 90.2%

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

   if 1.6500000000000001e-168 < y < 3.19999999999999995e-117

   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. *-commutative 98.6%

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

      2. associate-/l* 84.4%

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

      3. associate--l+ 84.4%

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

      4. fma-define 84.4%

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

      5. sub-neg 84.4%

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

      6. metadata-eval 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. exp-diff 53.6%

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

      2. sub-neg 53.6%

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

      3. metadata-eval 53.6%

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

      4. pow-to-exp 54.4%

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

      5. unpow-prod-up 54.4%

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

      6. exp-to-pow 54.4%

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

      7. associate-/l* 54.4%

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

      8. exp-to-pow 54.4%

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

      9. unpow-1 54.4%

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

   7. Applied egg-rr 54.4%

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

      1. associate-/r* 54.4%

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

      2. associate-*r/ 54.4%

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

      3. *-rgt-identity 54.4%

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

   9. Simplified 54.4%

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

   10. Taylor expanded in b around 0 100.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{elif}\;y \leq -115:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ t_2 := \frac{x}{y} \cdot e^{y \cdot \log z}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1300:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{a}^{t}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow a (+ t -1.0)) y) (exp b))))
        (t_2 (* (/ x y) (exp (* y (log z))))))
   (if (<= y -4.2e+172)
     t_2
     (if (<= y -2.45e+82)
       t_1
       (if (<= y -1300.0)
         (/ (* x (pow z y)) (* y a))
         (if (<= y 9e-169)
           t_1
           (if (<= y 3.3e-117)
             (/ (* x (pow a t)) (* y a))
             (if (<= y 2.5e-28)
               (* (/ x y) (/ (pow a t) (* a (exp b))))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(a, (t + -1.0)) / y) / exp(b));
	double t_2 = (x / y) * exp((y * log(z)));
	double tmp;
	if (y <= -4.2e+172) {
		tmp = t_2;
	} else if (y <= -2.45e+82) {
		tmp = t_1;
	} else if (y <= -1300.0) {
		tmp = (x * pow(z, y)) / (y * a);
	} else if (y <= 9e-169) {
		tmp = t_1;
	} else if (y <= 3.3e-117) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 2.5e-28) {
		tmp = (x / y) * (pow(a, t) / (a * exp(b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (((a ** (t + (-1.0d0))) / y) / exp(b))
    t_2 = (x / y) * exp((y * log(z)))
    if (y <= (-4.2d+172)) then
        tmp = t_2
    else if (y <= (-2.45d+82)) then
        tmp = t_1
    else if (y <= (-1300.0d0)) then
        tmp = (x * (z ** y)) / (y * a)
    else if (y <= 9d-169) then
        tmp = t_1
    else if (y <= 3.3d-117) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 2.5d-28) then
        tmp = (x / y) * ((a ** t) / (a * exp(b)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((Math.pow(a, (t + -1.0)) / y) / Math.exp(b));
	double t_2 = (x / y) * Math.exp((y * Math.log(z)));
	double tmp;
	if (y <= -4.2e+172) {
		tmp = t_2;
	} else if (y <= -2.45e+82) {
		tmp = t_1;
	} else if (y <= -1300.0) {
		tmp = (x * Math.pow(z, y)) / (y * a);
	} else if (y <= 9e-169) {
		tmp = t_1;
	} else if (y <= 3.3e-117) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 2.5e-28) {
		tmp = (x / y) * (Math.pow(a, t) / (a * Math.exp(b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(a, (t + -1.0)) / y) / math.exp(b))
	t_2 = (x / y) * math.exp((y * math.log(z)))
	tmp = 0
	if y <= -4.2e+172:
		tmp = t_2
	elif y <= -2.45e+82:
		tmp = t_1
	elif y <= -1300.0:
		tmp = (x * math.pow(z, y)) / (y * a)
	elif y <= 9e-169:
		tmp = t_1
	elif y <= 3.3e-117:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 2.5e-28:
		tmp = (x / y) * (math.pow(a, t) / (a * math.exp(b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / y) / exp(b)))
	t_2 = Float64(Float64(x / y) * exp(Float64(y * log(z))))
	tmp = 0.0
	if (y <= -4.2e+172)
		tmp = t_2;
	elseif (y <= -2.45e+82)
		tmp = t_1;
	elseif (y <= -1300.0)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(y * a));
	elseif (y <= 9e-169)
		tmp = t_1;
	elseif (y <= 3.3e-117)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 2.5e-28)
		tmp = Float64(Float64(x / y) * Float64((a ^ t) / Float64(a * exp(b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((a ^ (t + -1.0)) / y) / exp(b));
	t_2 = (x / y) * exp((y * log(z)));
	tmp = 0.0;
	if (y <= -4.2e+172)
		tmp = t_2;
	elseif (y <= -2.45e+82)
		tmp = t_1;
	elseif (y <= -1300.0)
		tmp = (x * (z ^ y)) / (y * a);
	elseif (y <= 9e-169)
		tmp = t_1;
	elseif (y <= 3.3e-117)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 2.5e-28)
		tmp = (x / y) * ((a ^ t) / (a * exp(b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+172], t$95$2, If[LessEqual[y, -2.45e+82], t$95$1, If[LessEqual[y, -1300.0], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-169], t$95$1, If[LessEqual[y, 3.3e-117], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-28], N[(N[(x / y), $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.2000000000000003e172 or 2.5000000000000001e-28 < 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* 94.1%

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

      3. associate--l+ 94.1%

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

      4. fma-define 94.1%

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

      5. sub-neg 94.1%

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

      6. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 82.4%

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

   if -4.2000000000000003e172 < y < -2.45e82 or -1300 < y < 8.9999999999999997e-169

   1. Initial program 95.6%

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

      1. associate-/l* 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 92.8%

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

      4. associate-/l* 91.9%

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

      5. *-commutative 91.9%

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

      6. exp-to-pow 91.9%

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

      7. exp-diff 80.6%

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

      8. *-commutative 80.6%

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

      9. exp-to-pow 81.7%

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

      10. sub-neg 81.7%

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

      11. metadata-eval 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in y around 0 82.4%

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

      1. associate-/r* 81.5%

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

      2. exp-to-pow 82.6%

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

      3. sub-neg 82.6%

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

      4. metadata-eval 82.6%

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

   7. Simplified 82.6%

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

   if -2.45e82 < y < -1300

   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 80.0%

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

   6. Taylor expanded in b around 0 90.2%

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

      1. *-commutative 90.2%

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

   8. Simplified 90.2%

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

   if 8.9999999999999997e-169 < y < 3.30000000000000015e-117

   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. *-commutative 98.6%

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

      2. associate-/l* 84.4%

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

      3. associate--l+ 84.4%

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

      4. fma-define 84.4%

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

      5. sub-neg 84.4%

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

      6. metadata-eval 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. exp-diff 53.6%

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

      2. sub-neg 53.6%

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

      3. metadata-eval 53.6%

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

      4. pow-to-exp 54.4%

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

      5. unpow-prod-up 54.4%

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

      6. exp-to-pow 54.4%

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

      7. associate-/l* 54.4%

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

      8. exp-to-pow 54.4%

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

      9. unpow-1 54.4%

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

   7. Applied egg-rr 54.4%

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

      1. associate-/r* 54.4%

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

      2. associate-*r/ 54.4%

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

      3. *-rgt-identity 54.4%

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

   9. Simplified 54.4%

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

   10. Taylor expanded in b around 0 100.0%

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

   if 3.30000000000000015e-117 < y < 2.5000000000000001e-28

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

      2. associate-/l* 97.8%

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

      3. associate--l+ 97.8%

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

      4. fma-define 97.8%

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

      5. sub-neg 97.8%

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

      6. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 97.8%

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

      1. exp-diff 92.1%

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

      2. sub-neg 92.1%

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

      3. metadata-eval 92.1%

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

      4. pow-to-exp 94.0%

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

      5. unpow-prod-up 94.0%

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

      6. exp-to-pow 94.0%

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

      7. associate-/l* 94.0%

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

      8. exp-to-pow 94.0%

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

      9. unpow-1 94.0%

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

   7. Applied egg-rr 94.0%

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

      1. associate-/r* 94.0%

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

      2. associate-*r/ 94.0%

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

      3. *-rgt-identity 94.0%

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

   9. Simplified 94.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{elif}\;y \leq -1300:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{a}^{t}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{x \cdot {a}^{t}}{y}\\ \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t + -1 \leq 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) (* a (* y (exp b)))))
        (t_2 (/ (* x (pow a t)) y)))
   (if (<= (+ t -1.0) -2e+28)
     t_2
     (if (<= (+ t -1.0) 2e+28)
       t_1
       (if (<= (+ t -1.0) 2e+208)
         t_2
         (if (<= (+ t -1.0) 1e+238) t_1 (* x (/ (pow a (+ t -1.0)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / (a * (y * exp(b)));
	double t_2 = (x * pow(a, t)) / y;
	double tmp;
	if ((t + -1.0) <= -2e+28) {
		tmp = t_2;
	} else if ((t + -1.0) <= 2e+28) {
		tmp = t_1;
	} else if ((t + -1.0) <= 2e+208) {
		tmp = t_2;
	} else if ((t + -1.0) <= 1e+238) {
		tmp = t_1;
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (z ** y)) / (a * (y * exp(b)))
    t_2 = (x * (a ** t)) / y
    if ((t + (-1.0d0)) <= (-2d+28)) then
        tmp = t_2
    else if ((t + (-1.0d0)) <= 2d+28) then
        tmp = t_1
    else if ((t + (-1.0d0)) <= 2d+208) then
        tmp = t_2
    else if ((t + (-1.0d0)) <= 1d+238) then
        tmp = t_1
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	double t_2 = (x * Math.pow(a, t)) / y;
	double tmp;
	if ((t + -1.0) <= -2e+28) {
		tmp = t_2;
	} else if ((t + -1.0) <= 2e+28) {
		tmp = t_1;
	} else if ((t + -1.0) <= 2e+208) {
		tmp = t_2;
	} else if ((t + -1.0) <= 1e+238) {
		tmp = t_1;
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	t_2 = (x * math.pow(a, t)) / y
	tmp = 0
	if (t + -1.0) <= -2e+28:
		tmp = t_2
	elif (t + -1.0) <= 2e+28:
		tmp = t_1
	elif (t + -1.0) <= 2e+208:
		tmp = t_2
	elif (t + -1.0) <= 1e+238:
		tmp = t_1
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))))
	t_2 = Float64(Float64(x * (a ^ t)) / y)
	tmp = 0.0
	if (Float64(t + -1.0) <= -2e+28)
		tmp = t_2;
	elseif (Float64(t + -1.0) <= 2e+28)
		tmp = t_1;
	elseif (Float64(t + -1.0) <= 2e+208)
		tmp = t_2;
	elseif (Float64(t + -1.0) <= 1e+238)
		tmp = t_1;
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / (a * (y * exp(b)));
	t_2 = (x * (a ^ t)) / y;
	tmp = 0.0;
	if ((t + -1.0) <= -2e+28)
		tmp = t_2;
	elseif ((t + -1.0) <= 2e+28)
		tmp = t_1;
	elseif ((t + -1.0) <= 2e+208)
		tmp = t_2;
	elseif ((t + -1.0) <= 1e+238)
		tmp = t_1;
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+28], t$95$2, If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+28], t$95$1, If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+208], t$95$2, If[LessEqual[N[(t + -1.0), $MachinePrecision], 1e+238], t$95$1, N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.99999999999999992e28 or 1.99999999999999992e28 < (-.f64 t #s(literal 1 binary64)) < 2e208

   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* 87.2%

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

      3. associate--l+ 87.2%

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

      4. fma-define 87.2%

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

      5. sub-neg 87.2%

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

      6. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 68.3%

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

      1. *-commutative 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in a around 0 81.2%

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

   if -1.99999999999999992e28 < (-.f64 t #s(literal 1 binary64)) < 1.99999999999999992e28 or 2e208 < (-.f64 t #s(literal 1 binary64)) < 1e238

   1. Initial program 96.1%

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

      1. associate-/l* 96.6%

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

      2. associate--l+ 96.6%

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

      3. exp-sum 88.3%

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

      4. associate-/l* 86.2%

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

      5. *-commutative 86.2%

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

      6. exp-to-pow 86.2%

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

      7. exp-diff 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 84.7%

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

      10. sub-neg 84.7%

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

      11. metadata-eval 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in t around 0 89.9%

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

   if 1e238 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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* 94.4%

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

      3. associate--l+ 94.4%

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

      4. fma-define 94.4%

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

      5. sub-neg 94.4%

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

      6. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 89.1%

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

   6. Taylor expanded in b around 0 89.1%

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

      1. associate-/l* 89.1%

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

      2. exp-to-pow 89.1%

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

      3. sub-neg 89.1%

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

      4. metadata-eval 89.1%

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

      5. +-commutative 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t + -1 \leq 10^{+238}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t + -1 \leq 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) (* a (* y (exp b))))))
   (if (<= (+ t -1.0) -1e+15)
     (* (exp (- (* (+ t -1.0) (log a)) b)) (/ x y))
     (if (<= (+ t -1.0) 2e+28)
       t_1
       (if (<= (+ t -1.0) 2e+208)
         (/ (* x (pow a t)) y)
         (if (<= (+ t -1.0) 1e+238) t_1 (* x (/ (pow a (+ t -1.0)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / (a * (y * exp(b)));
	double tmp;
	if ((t + -1.0) <= -1e+15) {
		tmp = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	} else if ((t + -1.0) <= 2e+28) {
		tmp = t_1;
	} else if ((t + -1.0) <= 2e+208) {
		tmp = (x * pow(a, t)) / y;
	} else if ((t + -1.0) <= 1e+238) {
		tmp = t_1;
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (z ** y)) / (a * (y * exp(b)))
    if ((t + (-1.0d0)) <= (-1d+15)) then
        tmp = exp((((t + (-1.0d0)) * log(a)) - b)) * (x / y)
    else if ((t + (-1.0d0)) <= 2d+28) then
        tmp = t_1
    else if ((t + (-1.0d0)) <= 2d+208) then
        tmp = (x * (a ** t)) / y
    else if ((t + (-1.0d0)) <= 1d+238) then
        tmp = t_1
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	double tmp;
	if ((t + -1.0) <= -1e+15) {
		tmp = Math.exp((((t + -1.0) * Math.log(a)) - b)) * (x / y);
	} else if ((t + -1.0) <= 2e+28) {
		tmp = t_1;
	} else if ((t + -1.0) <= 2e+208) {
		tmp = (x * Math.pow(a, t)) / y;
	} else if ((t + -1.0) <= 1e+238) {
		tmp = t_1;
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	tmp = 0
	if (t + -1.0) <= -1e+15:
		tmp = math.exp((((t + -1.0) * math.log(a)) - b)) * (x / y)
	elif (t + -1.0) <= 2e+28:
		tmp = t_1
	elif (t + -1.0) <= 2e+208:
		tmp = (x * math.pow(a, t)) / y
	elif (t + -1.0) <= 1e+238:
		tmp = t_1
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (Float64(t + -1.0) <= -1e+15)
		tmp = Float64(exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b)) * Float64(x / y));
	elseif (Float64(t + -1.0) <= 2e+28)
		tmp = t_1;
	elseif (Float64(t + -1.0) <= 2e+208)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	elseif (Float64(t + -1.0) <= 1e+238)
		tmp = t_1;
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / (a * (y * exp(b)));
	tmp = 0.0;
	if ((t + -1.0) <= -1e+15)
		tmp = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	elseif ((t + -1.0) <= 2e+28)
		tmp = t_1;
	elseif ((t + -1.0) <= 2e+208)
		tmp = (x * (a ^ t)) / y;
	elseif ((t + -1.0) <= 1e+238)
		tmp = t_1;
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+15], N[(N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+28], t$95$1, If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+208], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 1e+238], t$95$1, N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1e15

   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* 90.0%

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

      3. associate--l+ 90.0%

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

      4. fma-define 90.0%

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

      5. sub-neg 90.0%

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

      6. metadata-eval 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in y around 0 81.7%

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

   if -1e15 < (-.f64 t #s(literal 1 binary64)) < 1.99999999999999992e28 or 2e208 < (-.f64 t #s(literal 1 binary64)) < 1e238

   1. Initial program 96.0%

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

      1. associate-/l* 96.6%

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

      2. associate--l+ 96.6%

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

      3. exp-sum 88.1%

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

      4. associate-/l* 85.9%

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

      5. *-commutative 85.9%

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

      6. exp-to-pow 85.9%

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

      7. exp-diff 83.8%

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

      8. *-commutative 83.8%

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

      9. exp-to-pow 85.0%

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

      10. sub-neg 85.0%

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

      11. metadata-eval 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around 0 90.3%

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

   if 1.99999999999999992e28 < (-.f64 t #s(literal 1 binary64)) < 2e208

   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* 83.8%

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

      3. associate--l+ 83.8%

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

      4. fma-define 83.8%

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

      5. sub-neg 83.8%

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

      6. metadata-eval 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in t around inf 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in a around 0 81.4%

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

   if 1e238 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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* 94.4%

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

      3. associate--l+ 94.4%

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

      4. fma-define 94.4%

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

      5. sub-neg 94.4%

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

      6. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 89.1%

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

   6. Taylor expanded in b around 0 89.1%

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

      1. associate-/l* 89.1%

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

      2. exp-to-pow 89.1%

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

      3. sub-neg 89.1%

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

      4. metadata-eval 89.1%

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

      5. +-commutative 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t + -1 \leq 10^{+238}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;y \leq -255:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{elif}\;y \leq 17:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a (+ t -1.0)) y))))
   (if (<= y -255.0)
     (/ (* x (pow z y)) (* y a))
     (if (<= y -3.8e-143)
       t_1
       (if (<= y -5.8e-271)
         (/ (* x (/ (exp (- b)) a)) y)
         (if (<= y 17.0) t_1 (* (/ x y) (exp (* y (log z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, (t + -1.0)) / y);
	double tmp;
	if (y <= -255.0) {
		tmp = (x * pow(z, y)) / (y * a);
	} else if (y <= -3.8e-143) {
		tmp = t_1;
	} else if (y <= -5.8e-271) {
		tmp = (x * (exp(-b) / a)) / y;
	} else if (y <= 17.0) {
		tmp = t_1;
	} else {
		tmp = (x / y) * exp((y * log(z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** (t + (-1.0d0))) / y)
    if (y <= (-255.0d0)) then
        tmp = (x * (z ** y)) / (y * a)
    else if (y <= (-3.8d-143)) then
        tmp = t_1
    else if (y <= (-5.8d-271)) then
        tmp = (x * (exp(-b) / a)) / y
    else if (y <= 17.0d0) then
        tmp = t_1
    else
        tmp = (x / y) * exp((y * log(z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, (t + -1.0)) / y);
	double tmp;
	if (y <= -255.0) {
		tmp = (x * Math.pow(z, y)) / (y * a);
	} else if (y <= -3.8e-143) {
		tmp = t_1;
	} else if (y <= -5.8e-271) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else if (y <= 17.0) {
		tmp = t_1;
	} else {
		tmp = (x / y) * Math.exp((y * Math.log(z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, (t + -1.0)) / y)
	tmp = 0
	if y <= -255.0:
		tmp = (x * math.pow(z, y)) / (y * a)
	elif y <= -3.8e-143:
		tmp = t_1
	elif y <= -5.8e-271:
		tmp = (x * (math.exp(-b) / a)) / y
	elif y <= 17.0:
		tmp = t_1
	else:
		tmp = (x / y) * math.exp((y * math.log(z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ Float64(t + -1.0)) / y))
	tmp = 0.0
	if (y <= -255.0)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(y * a));
	elseif (y <= -3.8e-143)
		tmp = t_1;
	elseif (y <= -5.8e-271)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	elseif (y <= 17.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) * exp(Float64(y * log(z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ (t + -1.0)) / y);
	tmp = 0.0;
	if (y <= -255.0)
		tmp = (x * (z ^ y)) / (y * a);
	elseif (y <= -3.8e-143)
		tmp = t_1;
	elseif (y <= -5.8e-271)
		tmp = (x * (exp(-b) / a)) / y;
	elseif (y <= 17.0)
		tmp = t_1;
	else
		tmp = (x / y) * exp((y * log(z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -255.0], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-143], t$95$1, If[LessEqual[y, -5.8e-271], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 17.0], t$95$1, N[(N[(x / y), $MachinePrecision] * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -255

   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 67.9%

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

      4. associate-/l* 66.0%

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

      5. *-commutative 66.0%

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

      6. exp-to-pow 66.0%

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

      7. exp-diff 62.3%

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

      8. *-commutative 62.3%

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

      9. exp-to-pow 62.3%

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

      10. sub-neg 62.3%

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

      11. metadata-eval 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in t around 0 75.6%

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

   6. Taylor expanded in b around 0 81.3%

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

      1. *-commutative 81.3%

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

   8. Simplified 81.3%

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

   if -255 < y < -3.79999999999999981e-143 or -5.80000000000000028e-271 < y < 17

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-/l* 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 y around 0 94.8%

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

   6. Taylor expanded in b around 0 77.5%

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

      1. associate-/l* 79.2%

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

      2. exp-to-pow 80.6%

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

      3. sub-neg 80.6%

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

      4. metadata-eval 80.6%

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

      5. +-commutative 80.6%

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

   8. Simplified 80.6%

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

   if -3.79999999999999981e-143 < y < -5.80000000000000028e-271

   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* 86.8%

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

      3. associate--l+ 86.8%

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

      4. fma-define 86.8%

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

      5. sub-neg 86.8%

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

      6. metadata-eval 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around 0 98.8%

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

   6. Taylor expanded in t around 0 95.0%

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

      1. *-commutative 95.0%

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

      2. exp-diff 95.0%

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

      3. mul-1-neg 95.0%

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

      4. log-rec 95.0%

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

      5. rem-exp-log 96.2%

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

      6. associate-/l/ 96.2%

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

      7. associate-/r* 96.2%

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

      8. exp-neg 96.2%

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

   8. Simplified 96.2%

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

   if 17 < 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* 92.0%

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

      3. associate--l+ 92.0%

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

      4. fma-define 92.0%

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

      5. sub-neg 92.0%

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

      6. metadata-eval 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around inf 78.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -255:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{elif}\;y \leq 17:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{y \cdot \log z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -440 \lor \neg \left(t \leq 1.95 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -440.0) (not (<= t 1.95e+28)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -440.0) || !(t <= 1.95e+28)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-440.0d0)) .or. (.not. (t <= 1.95d+28))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -440.0) || !(t <= 1.95e+28)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -440.0) or not (t <= 1.95e+28):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -440.0) || !(t <= 1.95e+28))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -440.0) || ~((t <= 1.95e+28)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -440.0], N[Not[LessEqual[t, 1.95e+28]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -440 or 1.9499999999999999e28 < 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. *-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* 88.3%

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

      3. associate--l+ 88.3%

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

      4. fma-define 88.3%

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

      5. sub-neg 88.3%

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

      6. metadata-eval 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around 0 88.5%

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

   if -440 < t < 1.9499999999999999e28

   1. Initial program 95.6%

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

      1. associate-/l* 96.2%

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

      2. associate--l+ 96.2%

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

      3. exp-sum 90.0%

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

      4. associate-/l* 87.6%

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

      5. *-commutative 87.6%

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

      6. exp-to-pow 87.6%

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

      7. exp-diff 87.7%

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

      8. *-commutative 87.7%

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

      9. exp-to-pow 89.0%

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

      10. sub-neg 89.0%

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

      11. metadata-eval 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in t around 0 90.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -440 \lor \neg \left(t \leq 1.95 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ t_2 := \frac{x \cdot {a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-88}:\\ \;\;\;\;\frac{-1}{a \cdot \frac{y}{x \cdot b - x}}\\ \mathbf{elif}\;t \leq 4.2:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))) (t_2 (/ (* x (pow a t)) y)))
   (if (<= t -1.45e+55)
     t_2
     (if (<= t -6.4e-177)
       t_1
       (if (<= t -9.6e-276)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (if (<= t 1.4e-307)
           t_1
           (if (<= t 1.9e-88)
             (/ -1.0 (* a (/ y (- (* x b) x))))
             (if (<= t 4.2)
               (/
                (*
                 x
                 (+
                  (/ 1.0 a)
                  (*
                   b
                   (-
                    (/ -1.0 a)
                    (*
                     b
                     (-
                      (* 0.5 (/ -1.0 a))
                      (* -0.16666666666666666 (/ b a))))))))
                y)
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double t_2 = (x * pow(a, t)) / y;
	double tmp;
	if (t <= -1.45e+55) {
		tmp = t_2;
	} else if (t <= -6.4e-177) {
		tmp = t_1;
	} else if (t <= -9.6e-276) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (t <= 1.4e-307) {
		tmp = t_1;
	} else if (t <= 1.9e-88) {
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	} else if (t <= 4.2) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / 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 = x / (y * exp(b))
    t_2 = (x * (a ** t)) / y
    if (t <= (-1.45d+55)) then
        tmp = t_2
    else if (t <= (-6.4d-177)) then
        tmp = t_1
    else if (t <= (-9.6d-276)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else if (t <= 1.4d-307) then
        tmp = t_1
    else if (t <= 1.9d-88) then
        tmp = (-1.0d0) / (a * (y / ((x * b) - x)))
    else if (t <= 4.2d0) then
        tmp = (x * ((1.0d0 / a) + (b * (((-1.0d0) / a) - (b * ((0.5d0 * ((-1.0d0) / a)) - ((-0.16666666666666666d0) * (b / a)))))))) / 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 = x / (y * Math.exp(b));
	double t_2 = (x * Math.pow(a, t)) / y;
	double tmp;
	if (t <= -1.45e+55) {
		tmp = t_2;
	} else if (t <= -6.4e-177) {
		tmp = t_1;
	} else if (t <= -9.6e-276) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (t <= 1.4e-307) {
		tmp = t_1;
	} else if (t <= 1.9e-88) {
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	} else if (t <= 4.2) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	t_2 = (x * math.pow(a, t)) / y
	tmp = 0
	if t <= -1.45e+55:
		tmp = t_2
	elif t <= -6.4e-177:
		tmp = t_1
	elif t <= -9.6e-276:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	elif t <= 1.4e-307:
		tmp = t_1
	elif t <= 1.9e-88:
		tmp = -1.0 / (a * (y / ((x * b) - x)))
	elif t <= 4.2:
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	t_2 = Float64(Float64(x * (a ^ t)) / y)
	tmp = 0.0
	if (t <= -1.45e+55)
		tmp = t_2;
	elseif (t <= -6.4e-177)
		tmp = t_1;
	elseif (t <= -9.6e-276)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	elseif (t <= 1.4e-307)
		tmp = t_1;
	elseif (t <= 1.9e-88)
		tmp = Float64(-1.0 / Float64(a * Float64(y / Float64(Float64(x * b) - x))));
	elseif (t <= 4.2)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(-1.0 / a) - Float64(b * Float64(Float64(0.5 * Float64(-1.0 / a)) - Float64(-0.16666666666666666 * Float64(b / a)))))))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	t_2 = (x * (a ^ t)) / y;
	tmp = 0.0;
	if (t <= -1.45e+55)
		tmp = t_2;
	elseif (t <= -6.4e-177)
		tmp = t_1;
	elseif (t <= -9.6e-276)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	elseif (t <= 1.4e-307)
		tmp = t_1;
	elseif (t <= 1.9e-88)
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	elseif (t <= 4.2)
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.45e+55], t$95$2, If[LessEqual[t, -6.4e-177], t$95$1, If[LessEqual[t, -9.6e-276], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.4e-307], t$95$1, If[LessEqual[t, 1.9e-88], N[(-1.0 / N[(a * N[(y / N[(N[(x * b), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(-1.0 / a), $MachinePrecision] - N[(b * N[(N[(0.5 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] - N[(-0.16666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.4499999999999999e55 or 4.20000000000000018 < 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. *-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* 88.0%

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

      3. associate--l+ 88.0%

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

      4. fma-define 88.0%

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

      5. sub-neg 88.0%

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

      6. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in t around inf 69.5%

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

      1. *-commutative 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in a around 0 80.6%

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

   if -1.4499999999999999e55 < t < -6.3999999999999997e-177 or -9.5999999999999993e-276 < t < 1.4e-307

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

      2. associate-/l* 94.1%

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

      3. associate--l+ 94.1%

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

      4. fma-define 94.1%

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

      5. sub-neg 94.1%

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

      6. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in b around inf 59.0%

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

      1. neg-mul-1 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in b around inf 60.7%

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

      1. exp-neg 60.7%

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

      2. associate-*r/ 60.7%

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

      3. *-rgt-identity 60.7%

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

      4. associate-/r* 60.7%

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

      5. *-commutative 60.7%

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

   10. Simplified 60.7%

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

   if -6.3999999999999997e-177 < t < -9.5999999999999993e-276

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-/l* 94.9%

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

      3. associate--l+ 94.9%

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

      4. fma-define 94.9%

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

      5. sub-neg 94.9%

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

      6. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around 0 56.8%

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

   6. Taylor expanded in t around 0 56.8%

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

      1. *-commutative 56.8%

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

      2. exp-diff 56.8%

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

      3. mul-1-neg 56.8%

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

      4. log-rec 56.8%

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

      5. rem-exp-log 57.1%

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

      6. associate-/l/ 57.1%

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

      7. associate-/r* 57.1%

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

      8. exp-neg 57.1%

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

   8. Simplified 57.1%

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

   9. Taylor expanded in b around 0 52.0%

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

       1. +-commutative 52.0%

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

       2. mul-1-neg 52.0%

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

       3. unsub-neg 52.0%

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

       4. *-commutative 52.0%

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

       5. associate-/l* 52.0%

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

   11. Simplified 52.0%

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

   12. Taylor expanded in b around inf 57.3%

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

   if 1.4e-307 < t < 1.90000000000000006e-88

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 90.7%

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

      3. associate--l+ 90.7%

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

      4. fma-define 90.7%

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

      5. sub-neg 90.7%

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

      6. metadata-eval 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around 0 67.8%

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

   6. Taylor expanded in t around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. exp-diff 67.9%

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

      3. mul-1-neg 67.9%

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

      4. log-rec 67.9%

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

      5. rem-exp-log 70.0%

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

      6. associate-/l/ 70.0%

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

      7. associate-/r* 70.1%

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

      8. exp-neg 70.1%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in b around 0 41.9%

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

       1. +-commutative 41.9%

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

       2. mul-1-neg 41.9%

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

       3. unsub-neg 41.9%

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

       4. *-commutative 41.9%

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

       5. associate-/l* 41.9%

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

   11. Simplified 41.9%

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

       1. clear-num 41.8%

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

       2. inv-pow 41.8%

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

       3. associate-*r/ 41.7%

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

       4. *-commutative 41.7%

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

       5. sub-div 44.0%

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

   13. Applied egg-rr 44.0%

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

       1. unpow-1 44.0%

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

       2. associate-/r/ 58.7%

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

       3. *-commutative 58.7%

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

   15. Simplified 58.7%

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

   if 1.90000000000000006e-88 < t < 4.20000000000000018

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-/l* 74.6%

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

      3. associate--l+ 74.6%

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

      4. fma-define 74.6%

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

      5. sub-neg 74.6%

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

      6. metadata-eval 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around 0 80.9%

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

   6. Taylor expanded in t around 0 80.9%

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

      1. *-commutative 80.9%

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

      2. exp-diff 80.9%

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

      3. mul-1-neg 80.9%

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

      4. log-rec 80.9%

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

      5. rem-exp-log 82.7%

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

      6. associate-/l/ 82.7%

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

      7. associate-/r* 82.7%

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

      8. exp-neg 82.7%

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

   8. Simplified 82.7%

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

   9. Taylor expanded in b around 0 65.3%

      \[\leadsto \frac{\color{blue}{\left(b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{a} + 0.5 \cdot \frac{1}{a}\right) - \frac{1}{a}\right) + \frac{1}{a}\right)} \cdot x}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-276}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-88}:\\ \;\;\;\;\frac{-1}{a \cdot \frac{y}{x \cdot b - x}}\\ \mathbf{elif}\;t \leq 4.2:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{b}}{y}\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x \cdot a - a \cdot \left(x \cdot b\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-236}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+55} \lor \neg \left(b \leq 1.08 \cdot 10^{+186}\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp b) y))))
   (if (<= b -1.75e+53)
     (/
      (*
       x
       (+
        (/ 1.0 a)
        (*
         b
         (-
          (/ -1.0 a)
          (* b (- (* 0.5 (/ -1.0 a)) (* -0.16666666666666666 (/ b a))))))))
      y)
     (if (<= b -9e+14)
       t_1
       (if (<= b -1.75e-35)
         (/ (/ (- (* x a) (* a (* x b))) (* a a)) y)
         (if (<= b 2.8e-236)
           (/ (* b (- (/ x (* a b)) (/ x a))) y)
           (if (or (<= b 5.5e+55) (not (<= b 1.08e+186)))
             (* (/ x y) (/ 1.0 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 <= -1.75e+53) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= -9e+14) {
		tmp = t_1;
	} else if (b <= -1.75e-35) {
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y;
	} else if (b <= 2.8e-236) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if ((b <= 5.5e+55) || !(b <= 1.08e+186)) {
		tmp = (x / y) * (1.0 / 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 <= (-1.75d+53)) then
        tmp = (x * ((1.0d0 / a) + (b * (((-1.0d0) / a) - (b * ((0.5d0 * ((-1.0d0) / a)) - ((-0.16666666666666666d0) * (b / a)))))))) / y
    else if (b <= (-9d+14)) then
        tmp = t_1
    else if (b <= (-1.75d-35)) then
        tmp = (((x * a) - (a * (x * b))) / (a * a)) / y
    else if (b <= 2.8d-236) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else if ((b <= 5.5d+55) .or. (.not. (b <= 1.08d+186))) then
        tmp = (x / y) * (1.0d0 / 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 <= -1.75e+53) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= -9e+14) {
		tmp = t_1;
	} else if (b <= -1.75e-35) {
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y;
	} else if (b <= 2.8e-236) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if ((b <= 5.5e+55) || !(b <= 1.08e+186)) {
		tmp = (x / y) * (1.0 / 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 <= -1.75e+53:
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y
	elif b <= -9e+14:
		tmp = t_1
	elif b <= -1.75e-35:
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y
	elif b <= 2.8e-236:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	elif (b <= 5.5e+55) or not (b <= 1.08e+186):
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(b) / y))
	tmp = 0.0
	if (b <= -1.75e+53)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(-1.0 / a) - Float64(b * Float64(Float64(0.5 * Float64(-1.0 / a)) - Float64(-0.16666666666666666 * Float64(b / a)))))))) / y);
	elseif (b <= -9e+14)
		tmp = t_1;
	elseif (b <= -1.75e-35)
		tmp = Float64(Float64(Float64(Float64(x * a) - Float64(a * Float64(x * b))) / Float64(a * a)) / y);
	elseif (b <= 2.8e-236)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	elseif ((b <= 5.5e+55) || !(b <= 1.08e+186))
		tmp = Float64(Float64(x / y) * Float64(1.0 / 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 <= -1.75e+53)
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	elseif (b <= -9e+14)
		tmp = t_1;
	elseif (b <= -1.75e-35)
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y;
	elseif (b <= 2.8e-236)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	elseif ((b <= 5.5e+55) || ~((b <= 1.08e+186)))
		tmp = (x / y) * (1.0 / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e+53], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(-1.0 / a), $MachinePrecision] - N[(b * N[(N[(0.5 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] - N[(-0.16666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -9e+14], t$95$1, If[LessEqual[b, -1.75e-35], N[(N[(N[(N[(x * a), $MachinePrecision] - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.8e-236], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[b, 5.5e+55], N[Not[LessEqual[b, 1.08e+186]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.75000000000000009e53

   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* 91.7%

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

      3. associate--l+ 91.7%

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

      4. fma-define 91.7%

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

      5. sub-neg 91.7%

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

      6. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around 0 89.7%

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

   6. Taylor expanded in t around 0 87.7%

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

      1. *-commutative 87.7%

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

      2. exp-diff 87.7%

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

      3. mul-1-neg 87.7%

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

      4. log-rec 87.7%

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

      5. rem-exp-log 87.7%

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

      6. associate-/l/ 87.7%

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

      7. associate-/r* 87.7%

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

      8. exp-neg 87.7%

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

   8. Simplified 87.7%

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

   9. Taylor expanded in b around 0 87.9%

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

   if -1.75000000000000009e53 < b < -9e14 or 5.5000000000000004e55 < b < 1.08000000000000003e186

   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* 96.2%

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

      3. associate--l+ 96.2%

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

      4. fma-define 96.2%

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

      5. sub-neg 96.2%

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

      6. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in b around inf 43.1%

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

      1. neg-mul-1 43.1%

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

   7. Simplified 43.1%

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

      1. associate-*r/ 43.2%

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

      2. clear-num 43.2%

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

      3. *-commutative 43.2%

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

      4. add-sqr-sqrt 4.1%

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

      5. sqrt-unprod 43.2%

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

      6. sqr-neg 43.2%

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

      7. sqrt-unprod 39.1%

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

      8. add-sqr-sqrt 58.4%

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

   9. Applied egg-rr 58.4%

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

       1. associate-/r* 54.3%

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

       2. associate-/r/ 54.3%

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

       3. associate-/r/ 54.4%

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

       4. associate-*l/ 54.4%

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

       5. metadata-eval 54.4%

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

       6. distribute-lft-neg-in 54.4%

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

       7. neg-mul-1 54.4%

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

       8. remove-double-neg 54.4%

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

       9. associate-*l/ 58.4%

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

       10. associate-/l* 58.4%

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

   11. Simplified 58.4%

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

   if -9e14 < b < -1.74999999999999998e-35

   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 y around 0 73.4%

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

   6. Taylor expanded in t around 0 39.0%

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

      1. *-commutative 39.0%

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

      2. exp-diff 39.0%

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

      3. mul-1-neg 39.0%

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

      4. log-rec 39.0%

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

      5. rem-exp-log 39.0%

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

      6. associate-/l/ 39.0%

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

      7. associate-/r* 39.0%

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

      8. exp-neg 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in b around 0 21.9%

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

       1. +-commutative 21.9%

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

       2. mul-1-neg 21.9%

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

       3. unsub-neg 21.9%

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

       4. *-commutative 21.9%

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

       5. associate-/l* 21.9%

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

   11. Simplified 21.9%

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

       1. frac-2neg 21.9%

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

       2. associate-*r/ 21.9%

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

       3. *-commutative 21.9%

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

       4. frac-sub 48.0%

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

   13. Applied egg-rr 48.0%

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

   if -1.74999999999999998e-35 < b < 2.79999999999999986e-236

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 83.3%

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

      3. associate--l+ 83.3%

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

      4. fma-define 83.3%

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

      5. sub-neg 83.3%

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

      6. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 68.4%

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

   6. Taylor expanded in t around 0 42.0%

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

      1. *-commutative 42.0%

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

      2. exp-diff 42.0%

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

      3. mul-1-neg 42.0%

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

      4. log-rec 42.0%

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

      5. rem-exp-log 43.3%

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

      6. associate-/l/ 43.3%

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

      7. associate-/r* 43.3%

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

      8. exp-neg 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in b around 0 43.3%

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

       1. +-commutative 43.3%

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

       2. mul-1-neg 43.3%

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

       3. unsub-neg 43.3%

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

       4. *-commutative 43.3%

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

       5. associate-/l* 43.3%

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

   11. Simplified 43.3%

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

   12. Taylor expanded in b around inf 49.7%

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

   if 2.79999999999999986e-236 < b < 5.5000000000000004e55 or 1.08000000000000003e186 < b

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-/l* 90.4%

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

      3. associate--l+ 90.4%

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

      4. fma-define 90.4%

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

      5. sub-neg 90.4%

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

      6. metadata-eval 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around 0 80.7%

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

   6. Taylor expanded in t around 0 62.2%

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

      1. *-commutative 62.2%

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

      2. exp-diff 62.2%

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

      3. mul-1-neg 62.2%

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

      4. log-rec 62.2%

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

      5. rem-exp-log 63.0%

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

      6. associate-/l/ 63.0%

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

      7. associate-/r* 63.0%

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

      8. exp-neg 63.0%

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

   8. Simplified 63.0%

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

   9. Taylor expanded in b around 0 38.9%

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

       1. *-commutative 38.9%

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

   11. Simplified 38.9%

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

       1. *-un-lft-identity 38.9%

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

       2. *-commutative 38.9%

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

       3. times-frac 44.9%

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

   13. Applied egg-rr 44.9%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x \cdot a - a \cdot \left(x \cdot b\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-236}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+55} \lor \neg \left(b \leq 1.08 \cdot 10^{+186}\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y \cdot a}\\ t_2 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ t_3 := y \cdot e^{b}\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{t\_3}\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t\_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) (* y a)))
        (t_2 (* x (/ (pow a (+ t -1.0)) y)))
        (t_3 (* y (exp b))))
   (if (<= b -5.5e+84)
     (/ x t_3)
     (if (<= b -4.7e-299)
       t_1
       (if (<= b 4.6e-219)
         t_2
         (if (<= b 1.25e-127) t_1 (if (<= b 4.4e+92) t_2 (/ x (* a t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / (y * a);
	double t_2 = x * (pow(a, (t + -1.0)) / y);
	double t_3 = y * exp(b);
	double tmp;
	if (b <= -5.5e+84) {
		tmp = x / t_3;
	} else if (b <= -4.7e-299) {
		tmp = t_1;
	} else if (b <= 4.6e-219) {
		tmp = t_2;
	} else if (b <= 1.25e-127) {
		tmp = t_1;
	} else if (b <= 4.4e+92) {
		tmp = t_2;
	} else {
		tmp = x / (a * t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * (z ** y)) / (y * a)
    t_2 = x * ((a ** (t + (-1.0d0))) / y)
    t_3 = y * exp(b)
    if (b <= (-5.5d+84)) then
        tmp = x / t_3
    else if (b <= (-4.7d-299)) then
        tmp = t_1
    else if (b <= 4.6d-219) then
        tmp = t_2
    else if (b <= 1.25d-127) then
        tmp = t_1
    else if (b <= 4.4d+92) then
        tmp = t_2
    else
        tmp = x / (a * t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(z, y)) / (y * a);
	double t_2 = x * (Math.pow(a, (t + -1.0)) / y);
	double t_3 = y * Math.exp(b);
	double tmp;
	if (b <= -5.5e+84) {
		tmp = x / t_3;
	} else if (b <= -4.7e-299) {
		tmp = t_1;
	} else if (b <= 4.6e-219) {
		tmp = t_2;
	} else if (b <= 1.25e-127) {
		tmp = t_1;
	} else if (b <= 4.4e+92) {
		tmp = t_2;
	} else {
		tmp = x / (a * t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / (y * a)
	t_2 = x * (math.pow(a, (t + -1.0)) / y)
	t_3 = y * math.exp(b)
	tmp = 0
	if b <= -5.5e+84:
		tmp = x / t_3
	elif b <= -4.7e-299:
		tmp = t_1
	elif b <= 4.6e-219:
		tmp = t_2
	elif b <= 1.25e-127:
		tmp = t_1
	elif b <= 4.4e+92:
		tmp = t_2
	else:
		tmp = x / (a * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / Float64(y * a))
	t_2 = Float64(x * Float64((a ^ Float64(t + -1.0)) / y))
	t_3 = Float64(y * exp(b))
	tmp = 0.0
	if (b <= -5.5e+84)
		tmp = Float64(x / t_3);
	elseif (b <= -4.7e-299)
		tmp = t_1;
	elseif (b <= 4.6e-219)
		tmp = t_2;
	elseif (b <= 1.25e-127)
		tmp = t_1;
	elseif (b <= 4.4e+92)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(a * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / (y * a);
	t_2 = x * ((a ^ (t + -1.0)) / y);
	t_3 = y * exp(b);
	tmp = 0.0;
	if (b <= -5.5e+84)
		tmp = x / t_3;
	elseif (b <= -4.7e-299)
		tmp = t_1;
	elseif (b <= 4.6e-219)
		tmp = t_2;
	elseif (b <= 1.25e-127)
		tmp = t_1;
	elseif (b <= 4.4e+92)
		tmp = t_2;
	else
		tmp = x / (a * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+84], N[(x / t$95$3), $MachinePrecision], If[LessEqual[b, -4.7e-299], t$95$1, If[LessEqual[b, 4.6e-219], t$95$2, If[LessEqual[b, 1.25e-127], t$95$1, If[LessEqual[b, 4.4e+92], t$95$2, N[(x / N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.5000000000000004e84

   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* 92.9%

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

      3. associate--l+ 92.9%

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

      4. fma-define 92.9%

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

      5. sub-neg 92.9%

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

      6. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in b around inf 85.8%

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

      1. neg-mul-1 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in b around inf 90.6%

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

      1. exp-neg 90.6%

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

      2. associate-*r/ 90.6%

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

      3. *-rgt-identity 90.6%

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

      4. associate-/r* 90.6%

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

      5. *-commutative 90.6%

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

   10. Simplified 90.6%

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

   if -5.5000000000000004e84 < b < -4.6999999999999997e-299 or 4.59999999999999977e-219 < b < 1.2499999999999999e-127

   1. Initial program 97.9%

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

      1. associate-/l* 97.2%

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

      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 82.1%

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

      4. associate-/l* 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 76.4%

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

      8. *-commutative 76.4%

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

      9. exp-to-pow 77.4%

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

      10. sub-neg 77.4%

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

      11. metadata-eval 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in t around 0 72.3%

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

   6. Taylor expanded in b around 0 75.2%

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

      1. *-commutative 75.2%

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

   8. Simplified 75.2%

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

   if -4.6999999999999997e-299 < b < 4.59999999999999977e-219 or 1.2499999999999999e-127 < b < 4.39999999999999984e92

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-/l* 89.4%

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

      3. associate--l+ 89.4%

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

      4. fma-define 89.4%

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

      5. sub-neg 89.4%

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

      6. metadata-eval 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around 0 80.7%

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

   6. Taylor expanded in b around 0 72.5%

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

      1. associate-/l* 78.6%

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

      2. exp-to-pow 79.5%

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

      3. sub-neg 79.5%

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

      4. metadata-eval 79.5%

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

      5. +-commutative 79.5%

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

   8. Simplified 79.5%

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

   if 4.39999999999999984e92 < 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 y around 0 82.9%

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

      1. div-exp 54.3%

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

      2. exp-to-pow 54.3%

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

      3. sub-neg 54.3%

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

      4. metadata-eval 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in t around 0 85.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-127}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3400000000000:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x \cdot a - a \cdot \left(x \cdot b\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-234}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 22.5:\\ \;\;\;\;\frac{-1}{a \cdot \frac{y}{x \cdot b - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e+53)
   (/
    (*
     x
     (+
      (/ 1.0 a)
      (*
       b
       (-
        (/ -1.0 a)
        (* b (- (* 0.5 (/ -1.0 a)) (* -0.16666666666666666 (/ b a))))))))
    y)
   (if (<= b -3400000000000.0)
     (* x (/ (exp b) y))
     (if (<= b -1.7e-35)
       (/ (/ (- (* x a) (* a (* x b))) (* a a)) y)
       (if (<= b 6.2e-234)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (if (<= b 22.5)
           (/ -1.0 (* a (/ y (- (* x b) x))))
           (/ x (* y (exp b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+53) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= -3400000000000.0) {
		tmp = x * (exp(b) / y);
	} else if (b <= -1.7e-35) {
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y;
	} else if (b <= 6.2e-234) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (b <= 22.5) {
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	} else {
		tmp = x / (y * exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.75d+53)) then
        tmp = (x * ((1.0d0 / a) + (b * (((-1.0d0) / a) - (b * ((0.5d0 * ((-1.0d0) / a)) - ((-0.16666666666666666d0) * (b / a)))))))) / y
    else if (b <= (-3400000000000.0d0)) then
        tmp = x * (exp(b) / y)
    else if (b <= (-1.7d-35)) then
        tmp = (((x * a) - (a * (x * b))) / (a * a)) / y
    else if (b <= 6.2d-234) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else if (b <= 22.5d0) then
        tmp = (-1.0d0) / (a * (y / ((x * b) - x)))
    else
        tmp = x / (y * exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+53) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= -3400000000000.0) {
		tmp = x * (Math.exp(b) / y);
	} else if (b <= -1.7e-35) {
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y;
	} else if (b <= 6.2e-234) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (b <= 22.5) {
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+53:
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y
	elif b <= -3400000000000.0:
		tmp = x * (math.exp(b) / y)
	elif b <= -1.7e-35:
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y
	elif b <= 6.2e-234:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	elif b <= 22.5:
		tmp = -1.0 / (a * (y / ((x * b) - x)))
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+53)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(-1.0 / a) - Float64(b * Float64(Float64(0.5 * Float64(-1.0 / a)) - Float64(-0.16666666666666666 * Float64(b / a)))))))) / y);
	elseif (b <= -3400000000000.0)
		tmp = Float64(x * Float64(exp(b) / y));
	elseif (b <= -1.7e-35)
		tmp = Float64(Float64(Float64(Float64(x * a) - Float64(a * Float64(x * b))) / Float64(a * a)) / y);
	elseif (b <= 6.2e-234)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	elseif (b <= 22.5)
		tmp = Float64(-1.0 / Float64(a * Float64(y / Float64(Float64(x * b) - x))));
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e+53)
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	elseif (b <= -3400000000000.0)
		tmp = x * (exp(b) / y);
	elseif (b <= -1.7e-35)
		tmp = (((x * a) - (a * (x * b))) / (a * a)) / y;
	elseif (b <= 6.2e-234)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	elseif (b <= 22.5)
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+53], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(-1.0 / a), $MachinePrecision] - N[(b * N[(N[(0.5 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] - N[(-0.16666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3400000000000.0], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-35], N[(N[(N[(N[(x * a), $MachinePrecision] - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.2e-234], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 22.5], N[(-1.0 / N[(a * N[(y / N[(N[(x * b), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.75000000000000009e53

   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* 91.7%

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

      3. associate--l+ 91.7%

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

      4. fma-define 91.7%

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

      5. sub-neg 91.7%

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

      6. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around 0 89.7%

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

   6. Taylor expanded in t around 0 87.7%

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

      1. *-commutative 87.7%

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

      2. exp-diff 87.7%

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

      3. mul-1-neg 87.7%

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

      4. log-rec 87.7%

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

      5. rem-exp-log 87.7%

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

      6. associate-/l/ 87.7%

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

      7. associate-/r* 87.7%

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

      8. exp-neg 87.7%

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

   8. Simplified 87.7%

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

   9. Taylor expanded in b around 0 87.9%

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

   if -1.75000000000000009e53 < b < -3.4e12

   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* 83.3%

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

      3. associate--l+ 83.3%

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

      4. fma-define 83.3%

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

      5. sub-neg 83.3%

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

      6. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in b around inf 17.7%

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

      1. neg-mul-1 17.7%

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

   7. Simplified 17.7%

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

      1. associate-*r/ 18.0%

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

      2. clear-num 18.0%

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

      3. *-commutative 18.0%

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

      4. add-sqr-sqrt 18.0%

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

      5. sqrt-unprod 18.0%

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

      6. sqr-neg 18.0%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 83.6%

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

   9. Applied egg-rr 83.6%

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

       1. associate-/r* 66.9%

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

       2. associate-/r/ 66.9%

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

       3. associate-/r/ 66.9%

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

       4. associate-*l/ 66.9%

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

       5. metadata-eval 66.9%

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

       6. distribute-lft-neg-in 66.9%

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

       7. neg-mul-1 66.9%

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

       8. remove-double-neg 66.9%

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

       9. associate-*l/ 83.6%

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

       10. associate-/l* 83.6%

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

   11. Simplified 83.6%

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

   if -3.4e12 < b < -1.7000000000000001e-35

   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 y around 0 73.4%

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

   6. Taylor expanded in t around 0 39.0%

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

      1. *-commutative 39.0%

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

      2. exp-diff 39.0%

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

      3. mul-1-neg 39.0%

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

      4. log-rec 39.0%

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

      5. rem-exp-log 39.0%

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

      6. associate-/l/ 39.0%

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

      7. associate-/r* 39.0%

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

      8. exp-neg 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in b around 0 21.9%

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

       1. +-commutative 21.9%

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

       2. mul-1-neg 21.9%

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

       3. unsub-neg 21.9%

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

       4. *-commutative 21.9%

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

       5. associate-/l* 21.9%

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

   11. Simplified 21.9%

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

       1. frac-2neg 21.9%

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

       2. associate-*r/ 21.9%

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

       3. *-commutative 21.9%

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

       4. frac-sub 48.0%

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

   13. Applied egg-rr 48.0%

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

   if -1.7000000000000001e-35 < b < 6.2000000000000003e-234

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 83.3%

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

      3. associate--l+ 83.3%

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

      4. fma-define 83.3%

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

      5. sub-neg 83.3%

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

      6. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 68.4%

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

   6. Taylor expanded in t around 0 42.0%

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

      1. *-commutative 42.0%

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

      2. exp-diff 42.0%

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

      3. mul-1-neg 42.0%

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

      4. log-rec 42.0%

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

      5. rem-exp-log 43.3%

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

      6. associate-/l/ 43.3%

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

      7. associate-/r* 43.3%

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

      8. exp-neg 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in b around 0 43.3%

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

       1. +-commutative 43.3%

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

       2. mul-1-neg 43.3%

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

       3. unsub-neg 43.3%

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

       4. *-commutative 43.3%

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

       5. associate-/l* 43.3%

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

   11. Simplified 43.3%

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

   12. Taylor expanded in b around inf 49.7%

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

   if 6.2000000000000003e-234 < b < 22.5

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-/l* 92.9%

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

      3. associate--l+ 92.9%

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

      4. fma-define 92.9%

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

      5. sub-neg 92.9%

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

      6. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around 0 69.9%

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

   6. Taylor expanded in t around 0 44.6%

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

      1. *-commutative 44.6%

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

      2. exp-diff 44.6%

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

      3. mul-1-neg 44.6%

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

      4. log-rec 44.6%

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

      5. rem-exp-log 45.9%

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

      6. associate-/l/ 45.9%

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

      7. associate-/r* 45.9%

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

      8. exp-neg 45.9%

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

   8. Simplified 45.9%

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

   9. Taylor expanded in b around 0 38.8%

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

       1. +-commutative 38.8%

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

       2. mul-1-neg 38.8%

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

       3. unsub-neg 38.8%

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

       4. *-commutative 38.8%

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

       5. associate-/l* 38.8%

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

   11. Simplified 38.8%

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

       1. clear-num 38.8%

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

       2. inv-pow 38.8%

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

       3. associate-*r/ 38.8%

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

       4. *-commutative 38.8%

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

       5. sub-div 45.8%

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

   13. Applied egg-rr 45.8%

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

       1. unpow-1 45.8%

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

       2. associate-/r/ 57.5%

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

       3. *-commutative 57.5%

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

   15. Simplified 57.5%

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

   if 22.5 < 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* 91.2%

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

      3. associate--l+ 91.2%

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

      4. fma-define 91.2%

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

      5. sub-neg 91.2%

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

      6. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in b around inf 67.1%

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

      1. neg-mul-1 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in b around inf 75.8%

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

      1. exp-neg 75.8%

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

      2. associate-*r/ 75.8%

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

      3. *-rgt-identity 75.8%

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

      4. associate-/r* 75.8%

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

      5. *-commutative 75.8%

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

   10. Simplified 75.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3400000000000:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x \cdot a - a \cdot \left(x \cdot b\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-234}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 22.5:\\ \;\;\;\;\frac{-1}{a \cdot \frac{y}{x \cdot b - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e+52)
   (/
    (*
     x
     (+
      (/ 1.0 a)
      (*
       b
       (-
        (/ -1.0 a)
        (* b (- (* 0.5 (/ -1.0 a)) (* -0.16666666666666666 (/ b a))))))))
    y)
   (if (<= b 6e+85) (* x (/ (pow a (+ t -1.0)) y)) (/ x (* a (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+52) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= 6e+85) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.4d+52)) then
        tmp = (x * ((1.0d0 / a) + (b * (((-1.0d0) / a) - (b * ((0.5d0 * ((-1.0d0) / a)) - ((-0.16666666666666666d0) * (b / a)))))))) / y
    else if (b <= 6d+85) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+52) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= 6e+85) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.4e+52:
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y
	elif b <= 6e+85:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.4e+52)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(-1.0 / a) - Float64(b * Float64(Float64(0.5 * Float64(-1.0 / a)) - Float64(-0.16666666666666666 * Float64(b / a)))))))) / y);
	elseif (b <= 6e+85)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.4e+52)
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	elseif (b <= 6e+85)
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.4e+52], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(-1.0 / a), $MachinePrecision] - N[(b * N[(N[(0.5 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] - N[(-0.16666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6e+85], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.4e52

   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* 91.8%

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

      3. associate--l+ 91.8%

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

      4. fma-define 91.8%

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

      5. sub-neg 91.8%

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

      6. metadata-eval 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in y around 0 87.9%

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

   6. Taylor expanded in t around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. exp-diff 85.9%

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

      3. mul-1-neg 85.9%

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

      4. log-rec 85.9%

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

      5. rem-exp-log 85.9%

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

      6. associate-/l/ 85.9%

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

      7. associate-/r* 85.9%

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

      8. exp-neg 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in b around 0 86.2%

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

   if -6.4e52 < b < 6.0000000000000001e85

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-/l* 89.6%

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

      3. associate--l+ 89.6%

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

      4. fma-define 89.6%

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

      5. sub-neg 89.6%

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

      6. metadata-eval 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around 0 71.9%

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

   6. Taylor expanded in b around 0 67.9%

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

      1. associate-/l* 69.5%

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

      2. exp-to-pow 70.5%

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

      3. sub-neg 70.5%

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

      4. metadata-eval 70.5%

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

      5. +-commutative 70.5%

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

   8. Simplified 70.5%

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

   if 6.0000000000000001e85 < 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 y around 0 82.9%

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

      1. div-exp 54.3%

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

      2. exp-to-pow 54.3%

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

      3. sub-neg 54.3%

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

      4. metadata-eval 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in t around 0 85.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+56} \lor \neg \left(t \leq 2.5\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.85e+56) (not (<= t 2.5)))
   (/ (* x (pow a t)) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.85e+56) || !(t <= 2.5)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.85d+56)) .or. (.not. (t <= 2.5d0))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.85e+56) || !(t <= 2.5)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.85e+56) or not (t <= 2.5):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.85e+56) || !(t <= 2.5))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.85e+56) || ~((t <= 2.5)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.85e+56], N[Not[LessEqual[t, 2.5]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8500000000000001e56 or 2.5 < 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. *-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* 88.0%

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

      3. associate--l+ 88.0%

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

      4. fma-define 88.0%

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

      5. sub-neg 88.0%

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

      6. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in t around inf 69.5%

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

      1. *-commutative 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in a around 0 80.6%

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

   if -2.8500000000000001e56 < t < 2.5

   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. *-commutative 95.9%

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

      2. associate-/l* 90.7%

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

      3. associate--l+ 90.7%

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

      4. fma-define 90.7%

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

      5. sub-neg 90.7%

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

      6. metadata-eval 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around 0 67.0%

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

      1. div-exp 64.9%

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

      2. exp-to-pow 66.2%

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

      3. sub-neg 66.2%

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

      4. metadata-eval 66.2%

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

   7. Simplified 66.2%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

   8. Taylor expanded in t around 0 69.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+56} \lor \neg \left(t \leq 2.5\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-235}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 8500000000000:\\ \;\;\;\;\frac{-1}{a \cdot \frac{y}{x \cdot b - x}}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+184}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b \cdot \left(x + x \cdot \left(b \cdot -0.5\right)\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e-176)
   (/
    (*
     x
     (+
      (/ 1.0 a)
      (*
       b
       (-
        (/ -1.0 a)
        (* b (- (* 0.5 (/ -1.0 a)) (* -0.16666666666666666 (/ b a))))))))
    y)
   (if (<= b 2.2e-235)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (if (<= b 8500000000000.0)
       (/ -1.0 (* a (/ y (- (* x b) x))))
       (if (<= b 1.4e+184)
         (/ (- (/ x a) (/ (* b (+ x (* x (* b -0.5)))) a)) y)
         (* (/ x y) (/ 1.0 a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e-176) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= 2.2e-235) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (b <= 8500000000000.0) {
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	} else if (b <= 1.4e+184) {
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d-176)) then
        tmp = (x * ((1.0d0 / a) + (b * (((-1.0d0) / a) - (b * ((0.5d0 * ((-1.0d0) / a)) - ((-0.16666666666666666d0) * (b / a)))))))) / y
    else if (b <= 2.2d-235) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else if (b <= 8500000000000.0d0) then
        tmp = (-1.0d0) / (a * (y / ((x * b) - x)))
    else if (b <= 1.4d+184) then
        tmp = ((x / a) - ((b * (x + (x * (b * (-0.5d0))))) / a)) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e-176) {
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	} else if (b <= 2.2e-235) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else if (b <= 8500000000000.0) {
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	} else if (b <= 1.4e+184) {
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e-176:
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y
	elif b <= 2.2e-235:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	elif b <= 8500000000000.0:
		tmp = -1.0 / (a * (y / ((x * b) - x)))
	elif b <= 1.4e+184:
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e-176)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(-1.0 / a) - Float64(b * Float64(Float64(0.5 * Float64(-1.0 / a)) - Float64(-0.16666666666666666 * Float64(b / a)))))))) / y);
	elseif (b <= 2.2e-235)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	elseif (b <= 8500000000000.0)
		tmp = Float64(-1.0 / Float64(a * Float64(y / Float64(Float64(x * b) - x))));
	elseif (b <= 1.4e+184)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(b * Float64(x + Float64(x * Float64(b * -0.5)))) / a)) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e-176)
		tmp = (x * ((1.0 / a) + (b * ((-1.0 / a) - (b * ((0.5 * (-1.0 / a)) - (-0.16666666666666666 * (b / a)))))))) / y;
	elseif (b <= 2.2e-235)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	elseif (b <= 8500000000000.0)
		tmp = -1.0 / (a * (y / ((x * b) - x)));
	elseif (b <= 1.4e+184)
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e-176], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(-1.0 / a), $MachinePrecision] - N[(b * N[(N[(0.5 * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] - N[(-0.16666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.2e-235], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 8500000000000.0], N[(-1.0 / N[(a * N[(y / N[(N[(x * b), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+184], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(b * N[(x + N[(x * N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.19999999999999984e-176

   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. *-commutative 99.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 64.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 64.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 64.4%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 64.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 64.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 65.0%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 65.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 65.0%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 65.0%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 65.0%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 62.4%

      \[\leadsto \frac{\color{blue}{\left(b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{a} + 0.5 \cdot \frac{1}{a}\right) - \frac{1}{a}\right) + \frac{1}{a}\right)} \cdot x}{y} \]

   if -5.19999999999999984e-176 < b < 2.19999999999999984e-235

   1. Initial program 94.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 94.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 78.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 34.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 34.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 34.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 34.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 35.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 35.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 35.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 35.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 35.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 35.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 35.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 35.5%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 35.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 35.5%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 35.5%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 35.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 52.7%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 2.19999999999999984e-235 < b < 8.5e12

   1. Initial program 95.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 95.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 93.2%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 93.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 93.2%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 93.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 93.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 46.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 46.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 46.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 46.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 47.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 47.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 47.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 47.7%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 47.7%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 37.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 37.5%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 37.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 37.5%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 37.5%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 37.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]
   12. Step-by-step derivation

       1. clear-num 37.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{a} - x \cdot \frac{b}{a}}}} \]

       2. inv-pow 37.5%

          \[\leadsto \color{blue}{{\left(\frac{y}{\frac{x}{a} - x \cdot \frac{b}{a}}\right)}^{-1}} \]

       3. associate-*r/ 37.5%

          \[\leadsto {\left(\frac{y}{\frac{x}{a} - \color{blue}{\frac{x \cdot b}{a}}}\right)}^{-1} \]

       4. *-commutative 37.5%

          \[\leadsto {\left(\frac{y}{\frac{x}{a} - \frac{\color{blue}{b \cdot x}}{a}}\right)}^{-1} \]

       5. sub-div 44.4%

          \[\leadsto {\left(\frac{y}{\color{blue}{\frac{x - b \cdot x}{a}}}\right)}^{-1} \]

   13. Applied egg-rr 44.4%

       \[\leadsto \color{blue}{{\left(\frac{y}{\frac{x - b \cdot x}{a}}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 44.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x - b \cdot x}{a}}}} \]

       2. associate-/r/ 55.6%

          \[\leadsto \frac{1}{\color{blue}{\frac{y}{x - b \cdot x} \cdot a}} \]

       3. *-commutative 55.6%

          \[\leadsto \frac{1}{\frac{y}{x - \color{blue}{x \cdot b}} \cdot a} \]

   15. Simplified 55.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x - x \cdot b} \cdot a}} \]

   if 8.5e12 < b < 1.39999999999999995e184

   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 y around 0 87.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.0%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.0%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.0%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.0%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.0%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.0%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.1%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in a around -inf 42.2%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot \left(x + -0.5 \cdot \left(b \cdot x\right)\right)}{a}} + \frac{x}{a}}{y} \]
   11. Step-by-step derivation

       1. mul-1-neg 42.2%

          \[\leadsto \frac{\color{blue}{\left(-\frac{b \cdot \left(x + -0.5 \cdot \left(b \cdot x\right)\right)}{a}\right)} + \frac{x}{a}}{y} \]

       2. associate-*r* 42.2%

          \[\leadsto \frac{\left(-\frac{b \cdot \left(x + \color{blue}{\left(-0.5 \cdot b\right) \cdot x}\right)}{a}\right) + \frac{x}{a}}{y} \]

   12. Simplified 42.2%

       \[\leadsto \frac{\color{blue}{\left(-\frac{b \cdot \left(x + \left(-0.5 \cdot b\right) \cdot x\right)}{a}\right)} + \frac{x}{a}}{y} \]

   if 1.39999999999999995e184 < 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* 78.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 95.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 95.7%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 95.7%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 95.7%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 95.7%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 95.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 95.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 95.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 95.7%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 95.7%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 19.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 19.4%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 19.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 19.4%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 19.4%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 23.5%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 23.5%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{-1}{a} - b \cdot \left(0.5 \cdot \frac{-1}{a} - -0.16666666666666666 \cdot \frac{b}{a}\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-235}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 8500000000000:\\ \;\;\;\;\frac{-1}{a \cdot \frac{y}{x \cdot b - x}}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+184}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b \cdot \left(x + x \cdot \left(b \cdot -0.5\right)\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.2% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;a \leq 4.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+261}:\\ \;\;\;\;t\_1 - b \cdot \left(t\_1 - 0.5 \cdot \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b \cdot \left(x + x \cdot \left(b \cdot -0.5\right)\right)}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= a 4.5e+36)
     (/ (* x (+ (/ 1.0 a) (* b (+ (* (/ b a) 0.5) (/ -1.0 a))))) y)
     (if (<= a 3.3e+261)
       (- t_1 (* b (- t_1 (* 0.5 (/ (* x b) (* y a))))))
       (/ (- (/ x a) (/ (* b (+ x (* x (* b -0.5)))) a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (a <= 4.5e+36) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else if (a <= 3.3e+261) {
		tmp = t_1 - (b * (t_1 - (0.5 * ((x * b) / (y * a)))));
	} else {
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (a <= 4.5d+36) then
        tmp = (x * ((1.0d0 / a) + (b * (((b / a) * 0.5d0) + ((-1.0d0) / a))))) / y
    else if (a <= 3.3d+261) then
        tmp = t_1 - (b * (t_1 - (0.5d0 * ((x * b) / (y * a)))))
    else
        tmp = ((x / a) - ((b * (x + (x * (b * (-0.5d0))))) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (a <= 4.5e+36) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else if (a <= 3.3e+261) {
		tmp = t_1 - (b * (t_1 - (0.5 * ((x * b) / (y * a)))));
	} else {
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if a <= 4.5e+36:
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y
	elif a <= 3.3e+261:
		tmp = t_1 - (b * (t_1 - (0.5 * ((x * b) / (y * a)))))
	else:
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (a <= 4.5e+36)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(Float64(b / a) * 0.5) + Float64(-1.0 / a))))) / y);
	elseif (a <= 3.3e+261)
		tmp = Float64(t_1 - Float64(b * Float64(t_1 - Float64(0.5 * Float64(Float64(x * b) / Float64(y * a))))));
	else
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(b * Float64(x + Float64(x * Float64(b * -0.5)))) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (a <= 4.5e+36)
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	elseif (a <= 3.3e+261)
		tmp = t_1 - (b * (t_1 - (0.5 * ((x * b) / (y * a)))));
	else
		tmp = ((x / a) - ((b * (x + (x * (b * -0.5)))) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 4.5e+36], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[a, 3.3e+261], N[(t$95$1 - N[(b * N[(t$95$1 - N[(0.5 * N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(b * N[(x + N[(x * N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 4.49999999999999997e36

   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. *-commutative 99.2%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 58.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 58.0%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 58.0%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 58.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 58.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 58.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 58.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 58.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 58.7%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 58.7%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 45.4%

      \[\leadsto \frac{\color{blue}{\left(b \cdot \left(0.5 \cdot \frac{b}{a} - \frac{1}{a}\right) + \frac{1}{a}\right)} \cdot x}{y} \]

   if 4.49999999999999997e36 < a < 3.3e261

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 95.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.8%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 61.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 61.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 61.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 61.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 61.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 50.6%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{b \cdot x}{a \cdot y}\right) + \frac{x}{a \cdot y}} \]

   if 3.3e261 < a

   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. *-commutative 95.9%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 83.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 83.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 83.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 83.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 83.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 49.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 49.1%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 49.1%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 49.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 49.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 49.2%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 49.2%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 49.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 49.2%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 49.2%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 49.8%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in a around -inf 65.0%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot \left(x + -0.5 \cdot \left(b \cdot x\right)\right)}{a}} + \frac{x}{a}}{y} \]
   11. Step-by-step derivation

       1. mul-1-neg 65.0%

          \[\leadsto \frac{\color{blue}{\left(-\frac{b \cdot \left(x + -0.5 \cdot \left(b \cdot x\right)\right)}{a}\right)} + \frac{x}{a}}{y} \]

       2. associate-*r* 65.0%

          \[\leadsto \frac{\left(-\frac{b \cdot \left(x + \color{blue}{\left(-0.5 \cdot b\right) \cdot x}\right)}{a}\right) + \frac{x}{a}}{y} \]

   12. Simplified 65.0%

       \[\leadsto \frac{\color{blue}{\left(-\frac{b \cdot \left(x + \left(-0.5 \cdot b\right) \cdot x\right)}{a}\right)} + \frac{x}{a}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+261}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \left(\frac{x}{y \cdot a} - 0.5 \cdot \frac{x \cdot b}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b \cdot \left(x + x \cdot \left(b \cdot -0.5\right)\right)}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.4% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + b \cdot \left(0.5 \cdot \left(x \cdot b\right) - x\right)}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2e-18)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* (/ b a) 0.5) (/ -1.0 a))))) y)
   (/ (+ x (* b (- (* 0.5 (* x b)) x))) (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2e-18) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else {
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2d-18) then
        tmp = (x * ((1.0d0 / a) + (b * (((b / a) * 0.5d0) + ((-1.0d0) / a))))) / y
    else
        tmp = (x + (b * ((0.5d0 * (x * b)) - x))) / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2e-18) {
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	} else {
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2e-18:
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y
	else:
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2e-18)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(Float64(b / a) * 0.5) + Float64(-1.0 / a))))) / y);
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(0.5 * Float64(x * b)) - x))) / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2e-18)
		tmp = (x * ((1.0 / a) + (b * (((b / a) * 0.5) + (-1.0 / a))))) / y;
	else
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2e-18], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x + N[(b * N[(N[(0.5 * N[(x * b), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.0000000000000001e-18

   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. *-commutative 99.2%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 89.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 89.1%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 89.1%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 89.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 89.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 57.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 57.3%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 57.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 57.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 58.0%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 58.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 58.1%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 58.1%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 58.1%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 45.5%

      \[\leadsto \frac{\color{blue}{\left(b \cdot \left(0.5 \cdot \frac{b}{a} - \frac{1}{a}\right) + \frac{1}{a}\right)} \cdot x}{y} \]

   if 2.0000000000000001e-18 < a

   1. Initial program 96.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 58.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 58.8%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 58.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 58.8%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 59.4%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 59.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 59.4%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 59.4%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 59.4%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 42.2%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in a around 0 49.5%

       \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + 0.5 \cdot \left(b \cdot x\right)\right)}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(\frac{b}{a} \cdot 0.5 + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + b \cdot \left(0.5 \cdot \left(x \cdot b\right) - x\right)}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.8% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-236}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e+145)
   (- (/ x y) (/ (* x b) y))
   (if (<= b 9e-236)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (* (/ x y) (/ 1.0 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+145) {
		tmp = (x / y) - ((x * b) / y);
	} else if (b <= 9e-236) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.75d+145)) then
        tmp = (x / y) - ((x * b) / y)
    else if (b <= 9d-236) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e+145) {
		tmp = (x / y) - ((x * b) / y);
	} else if (b <= 9e-236) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e+145:
		tmp = (x / y) - ((x * b) / y)
	elif b <= 9e-236:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e+145)
		tmp = Float64(Float64(x / y) - Float64(Float64(x * b) / y));
	elseif (b <= 9e-236)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e+145)
		tmp = (x / y) - ((x * b) / y);
	elseif (b <= 9e-236)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e+145], N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-236], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7500000000000001e145

   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* 90.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 83.4%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 83.4%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 83.4%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 58.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   if -1.7500000000000001e145 < b < 8.99999999999999997e-236

   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. *-commutative 97.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 86.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 86.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 47.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 47.1%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 47.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 47.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 48.0%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 48.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 48.0%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 48.0%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 48.0%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 41.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 41.3%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 41.3%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 41.3%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 41.3%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 41.4%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 41.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 45.7%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 8.99999999999999997e-236 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.1%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.1%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.2%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.2%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.2%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 37.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 37.7%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 37.7%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 41.8%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 41.8%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-236}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.2% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(0.5 \cdot \frac{x \cdot b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-234}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e-176)
   (/ (+ (/ x a) (* b (* 0.5 (/ (* x b) a)))) y)
   (if (<= b 1.55e-234)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (* (/ x y) (/ 1.0 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e-176) {
		tmp = ((x / a) + (b * (0.5 * ((x * b) / a)))) / y;
	} else if (b <= 1.55e-234) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d-176)) then
        tmp = ((x / a) + (b * (0.5d0 * ((x * b) / a)))) / y
    else if (b <= 1.55d-234) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e-176) {
		tmp = ((x / a) + (b * (0.5 * ((x * b) / a)))) / y;
	} else if (b <= 1.55e-234) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e-176:
		tmp = ((x / a) + (b * (0.5 * ((x * b) / a)))) / y
	elif b <= 1.55e-234:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e-176)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(0.5 * Float64(Float64(x * b) / a)))) / y);
	elseif (b <= 1.55e-234)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e-176)
		tmp = ((x / a) + (b * (0.5 * ((x * b) / a)))) / y;
	elseif (b <= 1.55e-234)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e-176], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(0.5 * N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.55e-234], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.19999999999999984e-176

   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. *-commutative 99.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 64.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 64.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 64.4%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 64.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 64.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 65.0%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 65.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 65.0%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 65.0%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 65.0%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 53.3%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 53.3%

       \[\leadsto \frac{b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{a}\right)} + \frac{x}{a}}{y} \]

   if -5.19999999999999984e-176 < b < 1.5500000000000001e-234

   1. Initial program 94.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 94.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 78.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 34.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 34.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 34.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 34.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 35.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 35.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 35.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 35.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 35.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 35.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 35.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 35.5%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 35.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 35.5%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 35.5%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 35.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 52.7%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 1.5500000000000001e-234 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.1%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.1%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.2%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.2%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.2%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 37.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 37.7%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 37.7%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 41.8%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 41.8%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(0.5 \cdot \frac{x \cdot b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-234}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.2% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(x \cdot \left(\frac{b}{a} \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.7e-176)
   (/ (+ (/ x a) (* b (* x (* (/ b a) 0.5)))) y)
   (if (<= b 3.8e-233)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (* (/ x y) (/ 1.0 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.7e-176) {
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y;
	} else if (b <= 3.8e-233) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.7d-176)) then
        tmp = ((x / a) + (b * (x * ((b / a) * 0.5d0)))) / y
    else if (b <= 3.8d-233) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.7e-176) {
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y;
	} else if (b <= 3.8e-233) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.7e-176:
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y
	elif b <= 3.8e-233:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.7e-176)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(x * Float64(Float64(b / a) * 0.5)))) / y);
	elseif (b <= 3.8e-233)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.7e-176)
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y;
	elseif (b <= 3.8e-233)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.7e-176], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(x * N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.8e-233], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.69999999999999984e-176

   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. *-commutative 99.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 64.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 64.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 64.4%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 64.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 64.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 65.0%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 65.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 65.0%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 65.0%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 65.0%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 53.3%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 53.3%

       \[\leadsto \frac{b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{a}\right)} + \frac{x}{a}}{y} \]
   11. Step-by-step derivation

       1. associate-*l/ 54.2%

          \[\leadsto \frac{b \cdot \left(0.5 \cdot \color{blue}{\left(\frac{b}{a} \cdot x\right)}\right) + \frac{x}{a}}{y} \]

       2. *-commutative 54.2%

          \[\leadsto \frac{b \cdot \left(0.5 \cdot \color{blue}{\left(x \cdot \frac{b}{a}\right)}\right) + \frac{x}{a}}{y} \]

       3. *-commutative 54.2%

          \[\leadsto \frac{b \cdot \color{blue}{\left(\left(x \cdot \frac{b}{a}\right) \cdot 0.5\right)} + \frac{x}{a}}{y} \]

       4. associate-*l* 54.2%

          \[\leadsto \frac{b \cdot \color{blue}{\left(x \cdot \left(\frac{b}{a} \cdot 0.5\right)\right)} + \frac{x}{a}}{y} \]

       5. *-commutative 54.2%

          \[\leadsto \frac{b \cdot \left(x \cdot \color{blue}{\left(0.5 \cdot \frac{b}{a}\right)}\right) + \frac{x}{a}}{y} \]

   12. Simplified 54.2%

       \[\leadsto \frac{b \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \frac{b}{a}\right)\right)} + \frac{x}{a}}{y} \]

   if -4.69999999999999984e-176 < b < 3.8e-233

   1. Initial program 94.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 94.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 78.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 34.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 34.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 34.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 34.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 35.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 35.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 35.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 35.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 35.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 35.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 35.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 35.5%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 35.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 35.5%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 35.5%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 35.5%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 52.7%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 3.8e-233 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.1%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.1%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.2%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.2%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.2%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 37.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 37.7%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 37.7%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 41.8%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 41.8%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(x \cdot \left(\frac{b}{a} \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.2% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - b \cdot \left(\frac{1}{y} - 0.5 \cdot \frac{b}{y}\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-232}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+94)
   (* x (- (/ 1.0 y) (* b (- (/ 1.0 y) (* 0.5 (/ b y))))))
   (if (<= b 1.05e-232)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (* (/ x y) (/ 1.0 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+94) {
		tmp = x * ((1.0 / y) - (b * ((1.0 / y) - (0.5 * (b / y)))));
	} else if (b <= 1.05e-232) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d+94)) then
        tmp = x * ((1.0d0 / y) - (b * ((1.0d0 / y) - (0.5d0 * (b / y)))))
    else if (b <= 1.05d-232) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+94) {
		tmp = x * ((1.0 / y) - (b * ((1.0 / y) - (0.5 * (b / y)))));
	} else if (b <= 1.05e-232) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+94:
		tmp = x * ((1.0 / y) - (b * ((1.0 / y) - (0.5 * (b / y)))))
	elif b <= 1.05e-232:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+94)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b * Float64(Float64(1.0 / y) - Float64(0.5 * Float64(b / y))))));
	elseif (b <= 1.05e-232)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+94)
		tmp = x * ((1.0 / y) - (b * ((1.0 / y) - (0.5 * (b / y)))));
	elseif (b <= 1.05e-232)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+94], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b * N[(N[(1.0 / y), $MachinePrecision] - N[(0.5 * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-232], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.4999999999999998e94

   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* 92.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 85.5%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 85.5%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 85.5%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around inf 90.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   9. Step-by-step derivation

      1. associate-/l* 90.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-b}}{y}} \]

   10. Simplified 90.4%

       \[\leadsto \color{blue}{x \cdot \frac{e^{-b}}{y}} \]

   11. Taylor expanded in b around 0 81.3%

       \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(0.5 \cdot \frac{b}{y} - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   if -9.4999999999999998e94 < b < 1.05e-232

   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. *-commutative 97.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 85.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 85.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 85.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 85.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 85.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 42.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 42.3%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 42.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 42.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 43.3%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 43.3%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 43.3%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 43.3%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 43.3%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 39.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 39.7%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 39.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 39.7%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 39.7%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 39.7%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 44.5%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 1.05e-232 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.1%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.1%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.1%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.2%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.2%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.2%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.2%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 37.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 37.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 37.7%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 37.7%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 41.8%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 41.8%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - b \cdot \left(\frac{1}{y} - 0.5 \cdot \frac{b}{y}\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-232}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.5% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(x \cdot \left(\frac{b}{a} \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + b \cdot \left(0.5 \cdot \left(x \cdot b\right) - x\right)}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.15e-87)
   (/ (+ (/ x a) (* b (* x (* (/ b a) 0.5)))) y)
   (/ (+ x (* b (- (* 0.5 (* x b)) x))) (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.15e-87) {
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y;
	} else {
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.15d-87) then
        tmp = ((x / a) + (b * (x * ((b / a) * 0.5d0)))) / y
    else
        tmp = (x + (b * ((0.5d0 * (x * b)) - x))) / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.15e-87) {
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y;
	} else {
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.15e-87:
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y
	else:
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.15e-87)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(x * Float64(Float64(b / a) * 0.5)))) / y);
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(0.5 * Float64(x * b)) - x))) / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.15e-87)
		tmp = ((x / a) + (b * (x * ((b / a) * 0.5)))) / y;
	else
		tmp = (x + (b * ((0.5 * (x * b)) - x))) / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.15e-87], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(x * N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x + N[(b * N[(N[(0.5 * N[(x * b), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.1500000000000001e-87

   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. *-commutative 99.2%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 89.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 89.9%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 89.9%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 89.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 89.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 60.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 60.1%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 60.1%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 60.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 60.1%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 38.8%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 43.6%

       \[\leadsto \frac{b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{a}\right)} + \frac{x}{a}}{y} \]
   11. Step-by-step derivation

       1. associate-*l/ 44.5%

          \[\leadsto \frac{b \cdot \left(0.5 \cdot \color{blue}{\left(\frac{b}{a} \cdot x\right)}\right) + \frac{x}{a}}{y} \]

       2. *-commutative 44.5%

          \[\leadsto \frac{b \cdot \left(0.5 \cdot \color{blue}{\left(x \cdot \frac{b}{a}\right)}\right) + \frac{x}{a}}{y} \]

       3. *-commutative 44.5%

          \[\leadsto \frac{b \cdot \color{blue}{\left(\left(x \cdot \frac{b}{a}\right) \cdot 0.5\right)} + \frac{x}{a}}{y} \]

       4. associate-*l* 44.5%

          \[\leadsto \frac{b \cdot \color{blue}{\left(x \cdot \left(\frac{b}{a} \cdot 0.5\right)\right)} + \frac{x}{a}}{y} \]

       5. *-commutative 44.5%

          \[\leadsto \frac{b \cdot \left(x \cdot \color{blue}{\left(0.5 \cdot \frac{b}{a}\right)}\right) + \frac{x}{a}}{y} \]

   12. Simplified 44.5%

       \[\leadsto \frac{b \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \frac{b}{a}\right)\right)} + \frac{x}{a}}{y} \]

   if 1.1500000000000001e-87 < a

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      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 y around 0 75.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 56.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 56.4%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 56.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 56.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 57.1%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 57.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 57.1%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 57.1%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 57.1%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 41.0%

      \[\leadsto \frac{\color{blue}{b \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{b \cdot x}{a}\right) + \frac{x}{a}}}{y} \]

   10. Taylor expanded in a around 0 47.4%

       \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + 0.5 \cdot \left(b \cdot x\right)\right)}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(x \cdot \left(\frac{b}{a} \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + b \cdot \left(0.5 \cdot \left(x \cdot b\right) - x\right)}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 34.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+53)
   (/ (* x (/ b (- a))) y)
   (if (<= b 6.4e-232) (/ (/ x a) y) (* (/ x y) (/ 1.0 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+53) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= 6.4e-232) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.6d+53)) then
        tmp = (x * (b / -a)) / y
    else if (b <= 6.4d-232) then
        tmp = (x / a) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+53) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= 6.4e-232) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e+53:
		tmp = (x * (b / -a)) / y
	elif b <= 6.4e-232:
		tmp = (x / a) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+53)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= 6.4e-232)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.6e+53)
		tmp = (x * (b / -a)) / y;
	elseif (b <= 6.4e-232)
		tmp = (x / a) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+53], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.4e-232], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.6e53

   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* 91.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 91.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 91.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 91.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 91.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 89.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 87.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 87.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 87.4%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 87.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 87.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 87.4%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 87.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 87.4%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 87.4%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 87.4%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 49.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 49.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 49.1%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 49.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 49.1%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 49.1%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 49.1%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 49.1%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   13. Step-by-step derivation

       1. mul-1-neg 49.1%

          \[\leadsto \frac{\color{blue}{-\frac{b \cdot x}{a}}}{y} \]

       2. associate-*l/ 49.1%

          \[\leadsto \frac{-\color{blue}{\frac{b}{a} \cdot x}}{y} \]

       3. distribute-rgt-neg-in 49.1%

          \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-x\right)}}{y} \]

   14. Simplified 49.1%

       \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-x\right)}}{y} \]

   if -3.6e53 < b < 6.39999999999999973e-232

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.9%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 85.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 85.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 85.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 85.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 85.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 41.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 41.3%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 41.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 41.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 42.4%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 42.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 42.4%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 42.4%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 42.4%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 6.39999999999999973e-232 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 59.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 59.9%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 59.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 59.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 38.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 38.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 38.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 38.0%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 38.0%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 42.2%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 42.2%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 33.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e+99)
   (* x (- (/ 1.0 y) (/ b y)))
   (if (<= b 9.6e-232) (/ (/ x a) y) (* (/ x y) (/ 1.0 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+99) {
		tmp = x * ((1.0 / y) - (b / y));
	} else if (b <= 9.6e-232) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.05d+99)) then
        tmp = x * ((1.0d0 / y) - (b / y))
    else if (b <= 9.6d-232) then
        tmp = (x / a) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+99) {
		tmp = x * ((1.0 / y) - (b / y));
	} else if (b <= 9.6e-232) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e+99:
		tmp = x * ((1.0 / y) - (b / y))
	elif b <= 9.6e-232:
		tmp = (x / a) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e+99)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b / y)));
	elseif (b <= 9.6e-232)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.05e+99)
		tmp = x * ((1.0 / y) - (b / y));
	elseif (b <= 9.6e-232)
		tmp = (x / a) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e+99], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.6e-232], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05000000000000005e99

   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* 92.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 85.5%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 85.5%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 85.5%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around inf 90.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   9. Step-by-step derivation

      1. associate-/l* 90.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-b}}{y}} \]

   10. Simplified 90.4%

       \[\leadsto \color{blue}{x \cdot \frac{e^{-b}}{y}} \]

   11. Taylor expanded in b around 0 55.5%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{y} + \frac{1}{y}\right)} \]
   12. Step-by-step derivation

       1. +-commutative 55.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} + -1 \cdot \frac{b}{y}\right)} \]

       2. mul-1-neg 55.5%

          \[\leadsto x \cdot \left(\frac{1}{y} + \color{blue}{\left(-\frac{b}{y}\right)}\right) \]

       3. unsub-neg 55.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   13. Simplified 55.5%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   if -1.05000000000000005e99 < b < 9.59999999999999995e-232

   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. *-commutative 97.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 85.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 85.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 85.4%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 85.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 85.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 42.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 42.9%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 42.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 42.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 43.8%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 43.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 43.8%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 43.8%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 43.8%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 9.59999999999999995e-232 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 59.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 59.9%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 59.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 59.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 38.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 38.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 38.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 38.0%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 38.0%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 42.2%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 42.2%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 35.1% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.55 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.55e-230) (/ (/ (- x (* x b)) a) y) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.55e-230) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.55d-230) then
        tmp = ((x - (x * b)) / a) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.55e-230) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.55e-230:
		tmp = ((x - (x * b)) / a) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.55e-230)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.55e-230)
		tmp = ((x - (x * b)) / a) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.55e-230], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.55e-230

   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* 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 y around 0 76.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 56.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 56.5%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 56.5%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 56.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 56.5%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 57.2%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 57.2%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 57.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 57.2%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 57.2%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 42.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 42.7%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 42.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 42.7%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 42.7%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 42.7%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in a around 0 42.7%

       \[\leadsto \frac{\color{blue}{\frac{x - b \cdot x}{a}}}{y} \]

   if 1.55e-230 < b

   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. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 92.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 92.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 92.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 92.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 81.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 59.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 59.9%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 59.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 59.9%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 60.5%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 60.5%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 60.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 60.5%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 60.5%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 38.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 38.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 38.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 38.0%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 38.0%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 42.2%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 42.2%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.55 \cdot 10^{-230}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 32.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.5e-93) (/ (/ x a) y) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.5e-93) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.5d-93) then
        tmp = (x / a) / y
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.5e-93) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.5e-93:
		tmp = (x / a) / y
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.5e-93)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.5e-93)
		tmp = (x / a) / y;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.5e-93], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.5000000000000001e-93

   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. *-commutative 99.2%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 59.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 59.0%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 59.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 59.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 59.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 59.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 59.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 59.7%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 59.7%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 1.5000000000000001e-93 < a

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 57.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 57.3%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 57.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 57.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 57.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 57.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 57.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 57.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 57.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 39.4%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. div-inv 40.0%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

       2. *-commutative 40.0%

          \[\leadsto x \cdot \frac{1}{\color{blue}{a \cdot y}} \]

   13. Applied egg-rr 40.0%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 32.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 7.8e-56) (* (/ x y) (/ 1.0 a)) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 7.8e-56) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 7.8d-56) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 7.8e-56) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 7.8e-56:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 7.8e-56)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 7.8e-56)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 7.8e-56], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.8e-56

   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. *-commutative 99.2%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 58.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 58.4%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 58.4%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 58.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 58.4%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 59.2%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 59.2%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 59.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 59.2%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 59.2%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 32.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 32.3%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 32.3%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-un-lft-identity 32.3%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot a} \]

       2. *-commutative 32.3%

          \[\leadsto \frac{1 \cdot x}{\color{blue}{a \cdot y}} \]

       3. times-frac 41.4%

          \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   13. Applied egg-rr 41.4%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]

   if 7.8e-56 < a

   1. Initial program 96.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.5%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 57.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 57.6%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 57.6%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 57.6%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 58.1%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 58.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 58.1%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 58.1%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 58.1%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 39.1%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 39.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. div-inv 39.7%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

       2. *-commutative 39.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{a \cdot y}} \]

   13. Applied egg-rr 39.7%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 32.3% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e-93) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-93) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1d-93) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-93) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e-93:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e-93)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e-93)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e-93], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.999999999999999e-94

   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. *-commutative 99.2%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 59.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 59.0%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 59.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 59.0%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 59.7%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 59.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 59.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 59.7%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 59.7%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 9.999999999999999e-94 < a

   1. Initial program 96.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in t around 0 57.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
   7. Step-by-step derivation

      1. *-commutative 57.3%

         \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

      2. exp-diff 57.3%

         \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

      3. mul-1-neg 57.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

      4. log-rec 57.3%

         \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

      5. rem-exp-log 57.9%

         \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

      6. associate-/l/ 57.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

      7. associate-/r* 57.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

      8. exp-neg 57.9%

         \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

   8. Simplified 57.9%

      \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

   9. Taylor expanded in b around 0 39.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 39.4%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{-93}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 31.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 97.8%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 89.5%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 89.5%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 89.5%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 89.5%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 89.5%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 89.5%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 78.4%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

6. Taylor expanded in t around 0 58.0%

   \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]
7. Step-by-step derivation

   1. *-commutative 58.0%

      \[\leadsto \frac{\color{blue}{e^{-1 \cdot \log a - b} \cdot x}}{y} \]

   2. exp-diff 58.0%

      \[\leadsto \frac{\color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}} \cdot x}{y} \]

   3. mul-1-neg 58.0%

      \[\leadsto \frac{\frac{e^{\color{blue}{-\log a}}}{e^{b}} \cdot x}{y} \]

   4. log-rec 58.0%

      \[\leadsto \frac{\frac{e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}} \cdot x}{y} \]

   5. rem-exp-log 58.7%

      \[\leadsto \frac{\frac{\color{blue}{\frac{1}{a}}}{e^{b}} \cdot x}{y} \]

   6. associate-/l/ 58.7%

      \[\leadsto \frac{\color{blue}{\frac{1}{e^{b} \cdot a}} \cdot x}{y} \]

   7. associate-/r* 58.7%

      \[\leadsto \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{a}} \cdot x}{y} \]

   8. exp-neg 58.7%

      \[\leadsto \frac{\frac{\color{blue}{e^{-b}}}{a} \cdot x}{y} \]

8. Simplified 58.7%

   \[\leadsto \frac{\color{blue}{\frac{e^{-b}}{a} \cdot x}}{y} \]

9. Taylor expanded in b around 0 35.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 35.8%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

11. Simplified 35.8%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

12. Final simplification 35.8%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Alternative 29: 15.9% 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 97.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 97.8%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 89.5%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 89.5%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 89.5%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 89.5%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 89.5%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 89.5%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 42.0%

   \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
6. Step-by-step derivation

   1. neg-mul-1 42.0%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

7. Simplified 42.0%

   \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

8. Taylor expanded in b around 0 18.2%

   \[\leadsto \color{blue}{\frac{x}{y}} \]

9. Final simplification 18.2%

   \[\leadsto \frac{x}{y} \]
10. Add Preprocessing

Developer target: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024059 
(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))