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

Percentage Accurate: 98.3% → 98.3%

Time: 12.3s

Alternatives: 12

Speedup: 1.0×

• 47.4% 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

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (exp((((log(a) * (t - 1.0)) + (log(z) * y)) - b)) * 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 = (exp((((log(a) * (t - 1.0d0)) + (log(z) * y)) - b)) * x) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Final simplification 98.6%

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

Alternative 2: 76.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \log a \cdot \left(t - 1\right)\\ t_3 := \frac{t\_1}{y} \cdot x\\ \mathbf{if}\;t\_2 \leq -2000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -326:\\ \;\;\;\;\frac{t\_1}{e^{b} \cdot y} \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (* (log a) (- t 1.0)))
        (t_3 (* (/ t_1 y) x)))
   (if (<= t_2 -2000.0)
     t_3
     (if (<= t_2 -326.0)
       (* (/ t_1 (* (exp b) y)) x)
       (if (<= t_2 5e+98) (/ (/ (* (pow z y) x) a) y) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = log(a) * (t - 1.0);
	double t_3 = (t_1 / y) * x;
	double tmp;
	if (t_2 <= -2000.0) {
		tmp = t_3;
	} else if (t_2 <= -326.0) {
		tmp = (t_1 / (exp(b) * y)) * x;
	} else if (t_2 <= 5e+98) {
		tmp = ((pow(z, y) * x) / a) / y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = log(a) * (t - 1.0d0)
    t_3 = (t_1 / y) * x
    if (t_2 <= (-2000.0d0)) then
        tmp = t_3
    else if (t_2 <= (-326.0d0)) then
        tmp = (t_1 / (exp(b) * y)) * x
    else if (t_2 <= 5d+98) then
        tmp = (((z ** y) * x) / a) / y
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = Math.log(a) * (t - 1.0);
	double t_3 = (t_1 / y) * x;
	double tmp;
	if (t_2 <= -2000.0) {
		tmp = t_3;
	} else if (t_2 <= -326.0) {
		tmp = (t_1 / (Math.exp(b) * y)) * x;
	} else if (t_2 <= 5e+98) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = math.log(a) * (t - 1.0)
	t_3 = (t_1 / y) * x
	tmp = 0
	if t_2 <= -2000.0:
		tmp = t_3
	elif t_2 <= -326.0:
		tmp = (t_1 / (math.exp(b) * y)) * x
	elif t_2 <= 5e+98:
		tmp = ((math.pow(z, y) * x) / a) / y
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(log(a) * Float64(t - 1.0))
	t_3 = Float64(Float64(t_1 / y) * x)
	tmp = 0.0
	if (t_2 <= -2000.0)
		tmp = t_3;
	elseif (t_2 <= -326.0)
		tmp = Float64(Float64(t_1 / Float64(exp(b) * y)) * x);
	elseif (t_2 <= 5e+98)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = log(a) * (t - 1.0);
	t_3 = (t_1 / y) * x;
	tmp = 0.0;
	if (t_2 <= -2000.0)
		tmp = t_3;
	elseif (t_2 <= -326.0)
		tmp = (t_1 / (exp(b) * y)) * x;
	elseif (t_2 <= 5e+98)
		tmp = (((z ^ y) * x) / a) / y;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$2, -2000.0], t$95$3, If[LessEqual[t$95$2, -326.0], N[(N[(t$95$1 / N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+98], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -2e3 or 4.9999999999999998e98 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.8%

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

   if -2e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -326

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 54.2

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

   5. Applied rewrites 54.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 54.2

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

   7. Applied rewrites 54.2%

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

   8. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-/l/ N/A

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

      3. lower-/.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-exp.f64 86.1

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

   10. Applied rewrites 86.1%

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

   if -326 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4.9999999999999998e98

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 76.9

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

   5. Applied rewrites 76.9%

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

   7. Applied rewrites 77.0%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 80.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -2000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq -326:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b} \cdot y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -326:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -5e+19)
     t_2
     (if (<= t_1 -326.0)
       (/ (* (exp (- (- (log a)) b)) x) y)
       (if (<= t_1 5e+98) (/ (/ (* (pow z y) x) a) y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5e+19) {
		tmp = t_2;
	} else if (t_1 <= -326.0) {
		tmp = (exp((-log(a) - b)) * x) / y;
	} else if (t_1 <= 5e+98) {
		tmp = ((pow(z, y) * x) / 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 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-5d+19)) then
        tmp = t_2
    else if (t_1 <= (-326.0d0)) then
        tmp = (exp((-log(a) - b)) * x) / y
    else if (t_1 <= 5d+98) then
        tmp = (((z ** y) * x) / 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 = Math.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5e+19) {
		tmp = t_2;
	} else if (t_1 <= -326.0) {
		tmp = (Math.exp((-Math.log(a) - b)) * x) / y;
	} else if (t_1 <= 5e+98) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -5e+19:
		tmp = t_2
	elif t_1 <= -326.0:
		tmp = (math.exp((-math.log(a) - b)) * x) / y
	elif t_1 <= 5e+98:
		tmp = ((math.pow(z, y) * x) / a) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -5e+19)
		tmp = t_2;
	elseif (t_1 <= -326.0)
		tmp = Float64(Float64(exp(Float64(Float64(-log(a)) - b)) * x) / y);
	elseif (t_1 <= 5e+98)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -5e+19)
		tmp = t_2;
	elseif (t_1 <= -326.0)
		tmp = (exp((-log(a) - b)) * x) / y;
	elseif (t_1 <= 5e+98)
		tmp = (((z ^ y) * x) / a) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+19], t$95$2, If[LessEqual[t$95$1, -326.0], N[(N[(N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+98], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e19 or 4.9999999999999998e98 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 92.0%

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

   if -5e19 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -326

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.9%

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

   if -326 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4.9999999999999998e98

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 76.9

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

   5. Applied rewrites 76.9%

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

   7. Applied rewrites 77.0%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 80.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq -326:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -5e+19)
     t_2
     (if (<= t_1 5e+98) (/ (/ (* (pow z y) x) a) y) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5e+19) {
		tmp = t_2;
	} else if (t_1 <= 5e+98) {
		tmp = ((pow(z, y) * x) / 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 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-5d+19)) then
        tmp = t_2
    else if (t_1 <= 5d+98) then
        tmp = (((z ** y) * x) / 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 = Math.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5e+19) {
		tmp = t_2;
	} else if (t_1 <= 5e+98) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -5e+19:
		tmp = t_2
	elif t_1 <= 5e+98:
		tmp = ((math.pow(z, y) * x) / a) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -5e+19)
		tmp = t_2;
	elseif (t_1 <= 5e+98)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -5e+19)
		tmp = t_2;
	elseif (t_1 <= 5e+98)
		tmp = (((z ^ y) * x) / a) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+19], t$95$2, If[LessEqual[t$95$1, 5e+98], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e19 or 4.9999999999999998e98 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 92.0%

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

   if -5e19 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4.9999999999999998e98

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 71.5%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 75.2%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+159}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.3e+26)
   (/ (/ (* (pow z y) x) a) y)
   (if (<= y 5.9e+159)
     (/ (* (exp (- (* (log a) (- t 1.0)) b)) x) y)
     (/ (* (/ (pow z y) a) x) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+26) {
		tmp = ((pow(z, y) * x) / a) / y;
	} else if (y <= 5.9e+159) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = ((pow(z, y) / a) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.3d+26)) then
        tmp = (((z ** y) * x) / a) / y
    else if (y <= 5.9d+159) then
        tmp = (exp(((log(a) * (t - 1.0d0)) - b)) * x) / y
    else
        tmp = (((z ** y) / a) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+26) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else if (y <= 5.9e+159) {
		tmp = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = ((Math.pow(z, y) / a) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.3e+26:
		tmp = ((math.pow(z, y) * x) / a) / y
	elif y <= 5.9e+159:
		tmp = (math.exp(((math.log(a) * (t - 1.0)) - b)) * x) / y
	else:
		tmp = ((math.pow(z, y) / a) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.3e+26)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	elseif (y <= 5.9e+159)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * x) / y);
	else
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.3e+26)
		tmp = (((z ^ y) * x) / a) / y;
	elseif (y <= 5.9e+159)
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	else
		tmp = (((z ^ y) / a) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.3e+26], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 5.9e+159], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000001e26

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 67.7

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

   5. Applied rewrites 67.7%

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

   7. Applied rewrites 67.7%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 80.6%

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

   if -1.30000000000000001e26 < y < 5.89999999999999993e159

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 93.8

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

   5. Applied rewrites 93.8%

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

   if 5.89999999999999993e159 < 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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 92.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 93.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+159}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;t \leq 8.2:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t -5.5e+17)
     t_1
     (if (<= t 1.35e-99)
       (* (/ x y) (/ (pow z y) a))
       (if (<= t 8.2) (* (/ (exp (- b)) y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t <= -5.5e+17) {
		tmp = t_1;
	} else if (t <= 1.35e-99) {
		tmp = (x / y) * (pow(z, y) / a);
	} else if (t <= 8.2) {
		tmp = (exp(-b) / y) * x;
	} 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 = ((a ** (t - 1.0d0)) / y) * x
    if (t <= (-5.5d+17)) then
        tmp = t_1
    else if (t <= 1.35d-99) then
        tmp = (x / y) * ((z ** y) / a)
    else if (t <= 8.2d0) then
        tmp = (exp(-b) / y) * x
    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 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t <= -5.5e+17) {
		tmp = t_1;
	} else if (t <= 1.35e-99) {
		tmp = (x / y) * (Math.pow(z, y) / a);
	} else if (t <= 8.2) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t <= -5.5e+17:
		tmp = t_1
	elif t <= 1.35e-99:
		tmp = (x / y) * (math.pow(z, y) / a)
	elif t <= 8.2:
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t <= -5.5e+17)
		tmp = t_1;
	elseif (t <= 1.35e-99)
		tmp = Float64(Float64(x / y) * Float64((z ^ y) / a));
	elseif (t <= 8.2)
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t <= -5.5e+17)
		tmp = t_1;
	elseif (t <= 1.35e-99)
		tmp = (x / y) * ((z ^ y) / a);
	elseif (t <= 8.2)
		tmp = (exp(-b) / y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -5.5e+17], t$95$1, If[LessEqual[t, 1.35e-99], N[(N[(x / y), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5e17 or 8.1999999999999993 < 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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 72.6

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.5%

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

   if -5.5e17 < t < 1.35e-99

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 74.4

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

   10. Applied rewrites 74.4%

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

   if 1.35e-99 < t < 8.1999999999999993

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 67.4

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

   5. Applied rewrites 67.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 67.4

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

   7. Applied rewrites 67.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;t \leq 8.2:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 31.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log a \leq 80:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (log a) 80.0) (* (/ 1.0 a) (/ x y)) (* (/ (/ 1.0 a) y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (log(a) <= 80.0) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = ((1.0 / a) / y) * x;
	}
	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 (log(a) <= 80.0d0) then
        tmp = (1.0d0 / a) * (x / y)
    else
        tmp = ((1.0d0 / a) / y) * x
    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 (Math.log(a) <= 80.0) {
		tmp = (1.0 / a) * (x / y);
	} else {
		tmp = ((1.0 / a) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if math.log(a) <= 80.0:
		tmp = (1.0 / a) * (x / y)
	else:
		tmp = ((1.0 / a) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (log(a) <= 80.0)
		tmp = Float64(Float64(1.0 / a) * Float64(x / y));
	else
		tmp = Float64(Float64(Float64(1.0 / a) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (log(a) <= 80.0)
		tmp = (1.0 / a) * (x / y);
	else
		tmp = ((1.0 / a) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[Log[a], $MachinePrecision], 80.0], N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 a) < 80

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 35.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 36.4

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

   13. Applied rewrites 36.4%

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

   if 80 < (log.f64 a)

   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. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 55.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 30.4%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 32.0

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

   13. Applied rewrites 32.0%

       \[\leadsto \color{blue}{\frac{\frac{1}{a}}{y} \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 74.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+19}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.15e+68)
     t_1
     (if (<= b 2.15e+19) (* (/ (pow a (- t 1.0)) y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -1.15e+68) {
		tmp = t_1;
	} else if (b <= 2.15e+19) {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	} 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 = (exp(-b) / y) * x
    if (b <= (-1.15d+68)) then
        tmp = t_1
    else if (b <= 2.15d+19) then
        tmp = ((a ** (t - 1.0d0)) / y) * x
    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 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -1.15e+68) {
		tmp = t_1;
	} else if (b <= 2.15e+19) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -1.15e+68:
		tmp = t_1
	elif b <= 2.15e+19:
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -1.15e+68)
		tmp = t_1;
	elseif (b <= 2.15e+19)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -1.15e+68)
		tmp = t_1;
	elseif (b <= 2.15e+19)
		tmp = ((a ^ (t - 1.0)) / y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -1.15e+68], t$95$1, If[LessEqual[b, 2.15e+19], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e68 or 2.15e19 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 76.9

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

   5. Applied rewrites 76.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 76.9

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

   7. Applied rewrites 76.9%

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

   if -1.15e68 < b < 2.15e19

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 72.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+68}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+19}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -28000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 31000000:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -28000000000000.0)
     t_1
     (if (<= b 31000000.0) (/ (* (/ 1.0 a) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -28000000000000.0) {
		tmp = t_1;
	} else if (b <= 31000000.0) {
		tmp = ((1.0 / a) * x) / y;
	} 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 = (exp(-b) / y) * x
    if (b <= (-28000000000000.0d0)) then
        tmp = t_1
    else if (b <= 31000000.0d0) then
        tmp = ((1.0d0 / a) * x) / y
    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 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -28000000000000.0) {
		tmp = t_1;
	} else if (b <= 31000000.0) {
		tmp = ((1.0 / a) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -28000000000000.0:
		tmp = t_1
	elif b <= 31000000.0:
		tmp = ((1.0 / a) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -28000000000000.0)
		tmp = t_1;
	elseif (b <= 31000000.0)
		tmp = Float64(Float64(Float64(1.0 / a) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -28000000000000.0)
		tmp = t_1;
	elseif (b <= 31000000.0)
		tmp = ((1.0 / a) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -28000000000000.0], t$95$1, If[LessEqual[b, 31000000.0], N[(N[(N[(1.0 / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8e13 or 3.1e7 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 74.3

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

   5. Applied rewrites 74.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 74.3

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

   7. Applied rewrites 74.3%

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

   if -2.8e13 < b < 3.1e7

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 88.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 42.0%

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -28000000000000:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 31000000:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 32.0% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-128}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{x}}{\frac{1}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1e-128) (/ 1.0 (/ (/ y x) (/ 1.0 a))) (/ (* (/ 1.0 a) x) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e-128) {
		tmp = 1.0 / ((y / x) / (1.0 / a));
	} else {
		tmp = ((1.0 / a) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1d-128) then
        tmp = 1.0d0 / ((y / x) / (1.0d0 / a))
    else
        tmp = ((1.0d0 / a) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e-128) {
		tmp = 1.0 / ((y / x) / (1.0 / a));
	} else {
		tmp = ((1.0 / a) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1e-128:
		tmp = 1.0 / ((y / x) / (1.0 / a))
	else:
		tmp = ((1.0 / a) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1e-128)
		tmp = Float64(1.0 / Float64(Float64(y / x) / Float64(1.0 / a)));
	else
		tmp = Float64(Float64(Float64(1.0 / a) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1e-128)
		tmp = 1.0 / ((y / x) / (1.0 / a));
	else
		tmp = ((1.0 / a) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1e-128], N[(1.0 / N[(N[(y / x), $MachinePrecision] / N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000005e-128

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 70.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 59.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 33.3%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-/r* N/A

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

       6. lower-/.f64 N/A

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

   13. Applied rewrites 34.1%

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

   if 1.00000000000000005e-128 < x

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 64.4%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 32.8%

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{-128}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{x}}{\frac{1}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{a} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.8% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1}{a} \cdot x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (* (/ 1.0 a) x) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((1.0 / a) * 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 = ((1.0d0 / a) * x) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((1.0 / a) * x) / y;
}

Python

def code(x, y, z, t, a, b):
	return ((1.0 / a) * x) / y

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(1.0 / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Taylor expanded in b around 0

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. distribute-rgt-in N/A

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

   4. associate-+l+ N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. +-commutative N/A

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

   8. exp-sum N/A

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

   9. lower-*.f64 N/A

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

   10. *-commutative N/A

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

   11. exp-prod N/A

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

   12. lower-pow.f64 N/A

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

   13. rem-exp-log N/A

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

   14. +-commutative N/A

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

   15. mul-1-neg N/A

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

5. Applied rewrites 73.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 61.2%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 33.1%

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

12. Final simplification 33.1%

    \[\leadsto \frac{\frac{1}{a} \cdot x}{y} \]
13. Add Preprocessing

Alternative 12: 31.1% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{a} \cdot \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* (/ 1.0 a) (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (1.0 / a) * (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 = (1.0d0 / a) * (x / y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (1.0 / a) * (x / y);
}

Python

def code(x, y, z, t, a, b):
	return (1.0 / a) * (x / y)

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(1.0 / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Taylor expanded in b around 0

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. distribute-rgt-in N/A

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

   4. associate-+l+ N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. +-commutative N/A

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

   8. exp-sum N/A

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

   9. lower-*.f64 N/A

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

   10. *-commutative N/A

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

   11. exp-prod N/A

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

   12. lower-pow.f64 N/A

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

   13. rem-exp-log N/A

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

   14. +-commutative N/A

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

   15. mul-1-neg N/A

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

5. Applied rewrites 73.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 61.2%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 33.1%

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

    1. lift-/.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. *-commutative N/A

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

    4. associate-/l* N/A

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

    5. lower-*.f64 N/A

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

    6. lower-/.f64 32.1

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

13. Applied rewrites 32.1%

    \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y}} \]
14. Add Preprocessing

Developer Target 1: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))