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

Percentage Accurate: 98.4% → 98.4%

Time: 11.5s

Alternatives: 15

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% 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: 98.4% 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 97.8%

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

3. Final simplification 97.8%

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

Alternative 2: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \log a \cdot \left(t - 1\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\frac{t\_1}{y} \cdot x\\ \mathbf{elif}\;t\_2 \leq -342:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;t\_2 \leq -205:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;t\_2 \leq 2000000:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 \cdot x}{y}\\ \end{array} \end{array} \]

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))))
   (if (<= t_2 -1e+47)
     (* (/ t_1 y) x)
     (if (<= t_2 -342.0)
       (* (/ x y) (/ (pow z y) a))
       (if (<= t_2 -205.0)
         (* (/ (exp (- b)) y) x)
         (if (<= t_2 2000000.0)
           (/ (* (pow z y) x) (* a y))
           (/ (* t_1 x) y)))))))

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 tmp;
	if (t_2 <= -1e+47) {
		tmp = (t_1 / y) * x;
	} else if (t_2 <= -342.0) {
		tmp = (x / y) * (pow(z, y) / a);
	} else if (t_2 <= -205.0) {
		tmp = (exp(-b) / y) * x;
	} else if (t_2 <= 2000000.0) {
		tmp = (pow(z, y) * x) / (a * y);
	} else {
		tmp = (t_1 * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = log(a) * (t - 1.0d0)
    if (t_2 <= (-1d+47)) then
        tmp = (t_1 / y) * x
    else if (t_2 <= (-342.0d0)) then
        tmp = (x / y) * ((z ** y) / a)
    else if (t_2 <= (-205.0d0)) then
        tmp = (exp(-b) / y) * x
    else if (t_2 <= 2000000.0d0) then
        tmp = ((z ** y) * x) / (a * y)
    else
        tmp = (t_1 * 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 t_1 = Math.pow(a, (t - 1.0));
	double t_2 = Math.log(a) * (t - 1.0);
	double tmp;
	if (t_2 <= -1e+47) {
		tmp = (t_1 / y) * x;
	} else if (t_2 <= -342.0) {
		tmp = (x / y) * (Math.pow(z, y) / a);
	} else if (t_2 <= -205.0) {
		tmp = (Math.exp(-b) / y) * x;
	} else if (t_2 <= 2000000.0) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else {
		tmp = (t_1 * x) / y;
	}
	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)
	tmp = 0
	if t_2 <= -1e+47:
		tmp = (t_1 / y) * x
	elif t_2 <= -342.0:
		tmp = (x / y) * (math.pow(z, y) / a)
	elif t_2 <= -205.0:
		tmp = (math.exp(-b) / y) * x
	elif t_2 <= 2000000.0:
		tmp = (math.pow(z, y) * x) / (a * y)
	else:
		tmp = (t_1 * x) / y
	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))
	tmp = 0.0
	if (t_2 <= -1e+47)
		tmp = Float64(Float64(t_1 / y) * x);
	elseif (t_2 <= -342.0)
		tmp = Float64(Float64(x / y) * Float64((z ^ y) / a));
	elseif (t_2 <= -205.0)
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	elseif (t_2 <= 2000000.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	else
		tmp = Float64(Float64(t_1 * x) / y);
	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);
	tmp = 0.0;
	if (t_2 <= -1e+47)
		tmp = (t_1 / y) * x;
	elseif (t_2 <= -342.0)
		tmp = (x / y) * ((z ^ y) / a);
	elseif (t_2 <= -205.0)
		tmp = (exp(-b) / y) * x;
	elseif (t_2 <= 2000000.0)
		tmp = ((z ^ y) * x) / (a * y);
	else
		tmp = (t_1 * x) / y;
	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]}, If[LessEqual[t$95$2, -1e+47], N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, -342.0], N[(N[(x / y), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -205.0], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 2000000.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * x), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1e47

   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 75.6

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

   5. Applied rewrites 75.6%

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

   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 87.0%

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

   if -1e47 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -342

   1. Initial program 93.3%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 65.1

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

   5. Applied rewrites 65.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.2%

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

   if -342 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -205

   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 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 80.8

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

   5. Applied rewrites 80.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.8

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

   7. Applied rewrites 80.8%

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

   if -205 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e6

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.4%

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

   10. Applied rewrites 79.5%

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

   if 2e6 < (*.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 79.3

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

   5. Applied rewrites 79.3%

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

   7. Applied rewrites 68.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 96.3%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq -342:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq -205:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 2000000:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+17}:\\ \;\;\;\;\frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0)))
        (t_2 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= t_1 -1e+47)
     t_2
     (if (<= t_1 1e+17)
       (/ (* (exp (- (fma (log z) y (- (log a))) b)) x) 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 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (t_1 <= -1e+47) {
		tmp = t_2;
	} else if (t_1 <= 1e+17) {
		tmp = (exp((fma(log(z), y, -log(a)) - b)) * x) / 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(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (t_1 <= -1e+47)
		tmp = t_2;
	elseif (t_1 <= 1e+17)
		tmp = Float64(Float64(exp(Float64(fma(log(z), y, Float64(-log(a))) - b)) * x) / y);
	else
		tmp = t_2;
	end
	return 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[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+47], t$95$2, If[LessEqual[t$95$1, 1e+17], N[(N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $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)) < -1e47 or 1e17 < (*.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 97.1

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

   5. Applied rewrites 97.1%

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

   if -1e47 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e17

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 96.4

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

   5. Applied rewrites 96.4%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 10^{+17}:\\ \;\;\;\;\frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \log a \cdot \left(t - 1\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\frac{t\_1}{y} \cdot x\\ \mathbf{elif}\;t\_2 \leq 2000000:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 \cdot x}{y}\\ \end{array} \end{array} \]

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))))
   (if (<= t_2 -1e+47)
     (* (/ t_1 y) x)
     (if (<= t_2 2000000.0) (/ x (* (/ a (pow z y)) y)) (/ (* t_1 x) y)))))

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 tmp;
	if (t_2 <= -1e+47) {
		tmp = (t_1 / y) * x;
	} else if (t_2 <= 2000000.0) {
		tmp = x / ((a / pow(z, y)) * y);
	} else {
		tmp = (t_1 * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = log(a) * (t - 1.0d0)
    if (t_2 <= (-1d+47)) then
        tmp = (t_1 / y) * x
    else if (t_2 <= 2000000.0d0) then
        tmp = x / ((a / (z ** y)) * y)
    else
        tmp = (t_1 * 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 t_1 = Math.pow(a, (t - 1.0));
	double t_2 = Math.log(a) * (t - 1.0);
	double tmp;
	if (t_2 <= -1e+47) {
		tmp = (t_1 / y) * x;
	} else if (t_2 <= 2000000.0) {
		tmp = x / ((a / Math.pow(z, y)) * y);
	} else {
		tmp = (t_1 * x) / y;
	}
	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)
	tmp = 0
	if t_2 <= -1e+47:
		tmp = (t_1 / y) * x
	elif t_2 <= 2000000.0:
		tmp = x / ((a / math.pow(z, y)) * y)
	else:
		tmp = (t_1 * x) / y
	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))
	tmp = 0.0
	if (t_2 <= -1e+47)
		tmp = Float64(Float64(t_1 / y) * x);
	elseif (t_2 <= 2000000.0)
		tmp = Float64(x / Float64(Float64(a / (z ^ y)) * y));
	else
		tmp = Float64(Float64(t_1 * x) / y);
	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);
	tmp = 0.0;
	if (t_2 <= -1e+47)
		tmp = (t_1 / y) * x;
	elseif (t_2 <= 2000000.0)
		tmp = x / ((a / (z ^ y)) * y);
	else
		tmp = (t_1 * x) / y;
	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]}, If[LessEqual[t$95$2, -1e+47], N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 2000000.0], N[(x / N[(N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * x), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1e47

   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 75.6

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

   5. Applied rewrites 75.6%

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

   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 87.0%

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

   if -1e47 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e6

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 68.1

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

   5. Applied rewrites 68.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.8%

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

   10. Applied rewrites 74.1%

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

   if 2e6 < (*.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 79.3

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

   5. Applied rewrites 79.3%

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

   7. Applied rewrites 68.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 96.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 2000000:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;t \leq -10500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-298}:\\ \;\;\;\;\frac{\frac{e^{-b}}{a} \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= t -10500.0)
     t_1
     (if (<= t 2.35e-298)
       (/ (* (/ (exp (- b)) a) x) y)
       (if (<= t 1.35e+14) (/ x (* (/ a (pow z y)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (t <= -10500.0) {
		tmp = t_1;
	} else if (t <= 2.35e-298) {
		tmp = ((exp(-b) / a) * x) / y;
	} else if (t <= 1.35e+14) {
		tmp = x / ((a / pow(z, y)) * 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(((log(a) * t) - b)) * x) / y
    if (t <= (-10500.0d0)) then
        tmp = t_1
    else if (t <= 2.35d-298) then
        tmp = ((exp(-b) / a) * x) / y
    else if (t <= 1.35d+14) then
        tmp = x / ((a / (z ** y)) * 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(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (t <= -10500.0) {
		tmp = t_1;
	} else if (t <= 2.35e-298) {
		tmp = ((Math.exp(-b) / a) * x) / y;
	} else if (t <= 1.35e+14) {
		tmp = x / ((a / Math.pow(z, y)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if t <= -10500.0:
		tmp = t_1
	elif t <= 2.35e-298:
		tmp = ((math.exp(-b) / a) * x) / y
	elif t <= 1.35e+14:
		tmp = x / ((a / math.pow(z, y)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (t <= -10500.0)
		tmp = t_1;
	elseif (t <= 2.35e-298)
		tmp = Float64(Float64(Float64(exp(Float64(-b)) / a) * x) / y);
	elseif (t <= 1.35e+14)
		tmp = Float64(x / Float64(Float64(a / (z ^ y)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (t <= -10500.0)
		tmp = t_1;
	elseif (t <= 2.35e-298)
		tmp = ((exp(-b) / a) * x) / y;
	elseif (t <= 1.35e+14)
		tmp = x / ((a / (z ^ y)) * 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[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -10500.0], t$95$1, If[LessEqual[t, 2.35e-298], N[(N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.35e+14], N[(x / N[(N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -10500 or 1.35e14 < 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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 94.6

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

   5. Applied rewrites 94.6%

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

   if -10500 < t < 2.35000000000000019e-298

   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 y around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. exp-prod N/A

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

      4. lower-pow.f64 N/A

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

      5. rem-exp-log N/A

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

      6. lower--.f64 N/A

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

      7. lower-exp.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.0%

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

   if 2.35000000000000019e-298 < t < 1.35e14

   1. Initial program 92.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 83.2

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 84.4%

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

   10. Applied rewrites 88.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -10500:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-298}:\\ \;\;\;\;\frac{\frac{e^{-b}}{a} \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+136}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (/ a (pow z y)) y))))
   (if (<= y -1.55e+82)
     t_1
     (if (<= y 2.2e+136) (/ (* (exp (- (* (log a) (- t 1.0)) b)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a / pow(z, y)) * y);
	double tmp;
	if (y <= -1.55e+82) {
		tmp = t_1;
	} else if (y <= 2.2e+136) {
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * 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 = x / ((a / (z ** y)) * y)
    if (y <= (-1.55d+82)) then
        tmp = t_1
    else if (y <= 2.2d+136) then
        tmp = (exp(((log(a) * (t - 1.0d0)) - b)) * 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 = x / ((a / Math.pow(z, y)) * y);
	double tmp;
	if (y <= -1.55e+82) {
		tmp = t_1;
	} else if (y <= 2.2e+136) {
		tmp = (Math.exp(((Math.log(a) * (t - 1.0)) - b)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a / math.pow(z, y)) * y)
	tmp = 0
	if y <= -1.55e+82:
		tmp = t_1
	elif y <= 2.2e+136:
		tmp = (math.exp(((math.log(a) * (t - 1.0)) - b)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a / (z ^ y)) * y))
	tmp = 0.0
	if (y <= -1.55e+82)
		tmp = t_1;
	elseif (y <= 2.2e+136)
		tmp = Float64(Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a / (z ^ y)) * y);
	tmp = 0.0;
	if (y <= -1.55e+82)
		tmp = t_1;
	elseif (y <= 2.2e+136)
		tmp = (exp(((log(a) * (t - 1.0)) - b)) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+82], t$95$1, If[LessEqual[y, 2.2e+136], N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000016e82 or 2.1999999999999999e136 < 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

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.8%

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

   10. Applied rewrites 88.5%

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

   if -1.55000000000000016e82 < y < 2.1999999999999999e136

   1. Initial program 96.9%

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

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+136}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= b -9.2e-7)
     t_1
     (if (<= b 7e+17) (* (/ (pow a (- t 1.0)) y) (* (pow z y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -9.2e-7) {
		tmp = t_1;
	} else if (b <= 7e+17) {
		tmp = (pow(a, (t - 1.0)) / y) * (pow(z, 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(((log(a) * t) - b)) * x) / y
    if (b <= (-9.2d-7)) then
        tmp = t_1
    else if (b <= 7d+17) then
        tmp = ((a ** (t - 1.0d0)) / y) * ((z ** 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(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -9.2e-7) {
		tmp = t_1;
	} else if (b <= 7e+17) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * (Math.pow(z, y) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if b <= -9.2e-7:
		tmp = t_1
	elif b <= 7e+17:
		tmp = (math.pow(a, (t - 1.0)) / y) * (math.pow(z, y) * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (b <= -9.2e-7)
		tmp = t_1;
	elseif (b <= 7e+17)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * Float64((z ^ y) * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (b <= -9.2e-7)
		tmp = t_1;
	elseif (b <= 7e+17)
		tmp = ((a ^ (t - 1.0)) / y) * ((z ^ 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[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -9.2e-7], t$95$1, If[LessEqual[b, 7e+17], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.1999999999999998e-7 or 7e17 < 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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 89.1

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

   5. Applied rewrites 89.1%

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

   if -9.1999999999999998e-7 < b < 7e17

   1. Initial program 95.7%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 90.1

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

   5. Applied rewrites 90.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 31.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log a \leq -194:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{-1}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (log a) -194.0) (/ (/ x a) y) (* (/ (pow a -1.0) y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (log(a) <= -194.0) {
		tmp = (x / a) / y;
	} else {
		tmp = (pow(a, -1.0) / 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) <= (-194.0d0)) then
        tmp = (x / a) / y
    else
        tmp = ((a ** (-1.0d0)) / 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) <= -194.0) {
		tmp = (x / a) / y;
	} else {
		tmp = (Math.pow(a, -1.0) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if math.log(a) <= -194.0:
		tmp = (x / a) / y
	else:
		tmp = (math.pow(a, -1.0) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (log(a) <= -194.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64((a ^ -1.0) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (log(a) <= -194.0)
		tmp = (x / a) / y;
	else
		tmp = ((a ^ -1.0) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[Log[a], $MachinePrecision], -194.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, -1.0], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 a) < -194

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 80.7

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

   5. Applied rewrites 80.7%

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

   7. Applied rewrites 70.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 69.5%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 38.4%

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

   if -194 < (log.f64 a)

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 67.9

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

   5. Applied rewrites 67.9%

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

   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 64.5%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 33.6%

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

Alternative 9: 75.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t \leq -240000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-298}:\\ \;\;\;\;\frac{\frac{e^{-b}}{a} \cdot x}{y}\\ \mathbf{elif}\;t \leq 14800000:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t -240000.0)
     t_1
     (if (<= t 2.35e-298)
       (/ (* (/ (exp (- b)) a) x) y)
       (if (<= t 14800000.0) (/ x (* (/ a (pow z y)) y)) 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 <= -240000.0) {
		tmp = t_1;
	} else if (t <= 2.35e-298) {
		tmp = ((exp(-b) / a) * x) / y;
	} else if (t <= 14800000.0) {
		tmp = x / ((a / pow(z, y)) * 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 = ((a ** (t - 1.0d0)) / y) * x
    if (t <= (-240000.0d0)) then
        tmp = t_1
    else if (t <= 2.35d-298) then
        tmp = ((exp(-b) / a) * x) / y
    else if (t <= 14800000.0d0) then
        tmp = x / ((a / (z ** y)) * 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.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t <= -240000.0) {
		tmp = t_1;
	} else if (t <= 2.35e-298) {
		tmp = ((Math.exp(-b) / a) * x) / y;
	} else if (t <= 14800000.0) {
		tmp = x / ((a / Math.pow(z, y)) * y);
	} 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 <= -240000.0:
		tmp = t_1
	elif t <= 2.35e-298:
		tmp = ((math.exp(-b) / a) * x) / y
	elif t <= 14800000.0:
		tmp = x / ((a / math.pow(z, y)) * y)
	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 <= -240000.0)
		tmp = t_1;
	elseif (t <= 2.35e-298)
		tmp = Float64(Float64(Float64(exp(Float64(-b)) / a) * x) / y);
	elseif (t <= 14800000.0)
		tmp = Float64(x / Float64(Float64(a / (z ^ y)) * y));
	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 <= -240000.0)
		tmp = t_1;
	elseif (t <= 2.35e-298)
		tmp = ((exp(-b) / a) * x) / y;
	elseif (t <= 14800000.0)
		tmp = x / ((a / (z ^ y)) * 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[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -240000.0], t$95$1, If[LessEqual[t, 2.35e-298], N[(N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 14800000.0], N[(x / N[(N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e5 or 1.48e7 < 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 76.7

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

   5. Applied rewrites 76.7%

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

   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 90.2%

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

   if -2.4e5 < t < 2.35000000000000019e-298

   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 y around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. exp-prod N/A

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

      4. lower-pow.f64 N/A

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

      5. rem-exp-log N/A

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

      6. lower--.f64 N/A

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

      7. lower-exp.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.0%

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

   if 2.35000000000000019e-298 < t < 1.48e7

   1. Initial program 92.7%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 82.7

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 83.9%

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

   10. Applied rewrites 88.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -240000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-298}:\\ \;\;\;\;\frac{\frac{e^{-b}}{a} \cdot x}{y}\\ \mathbf{elif}\;t \leq 14800000:\\ \;\;\;\;\frac{x}{\frac{a}{{z}^{y}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.1e+31)
     t_1
     (if (<= b 3.4e-5) (* (/ (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 <= -1.1e+31) {
		tmp = t_1;
	} else if (b <= 3.4e-5) {
		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 <= (-1.1d+31)) then
        tmp = t_1
    else if (b <= 3.4d-5) 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 <= -1.1e+31) {
		tmp = t_1;
	} else if (b <= 3.4e-5) {
		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 <= -1.1e+31:
		tmp = t_1
	elif b <= 3.4e-5:
		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 <= -1.1e+31)
		tmp = t_1;
	elseif (b <= 3.4e-5)
		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 <= -1.1e+31)
		tmp = t_1;
	elseif (b <= 3.4e-5)
		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, -1.1e+31], t$95$1, If[LessEqual[b, 3.4e-5], 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 < -1.10000000000000005e31 or 3.4e-5 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 79.7

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

   5. Applied rewrites 79.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 79.7

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

   7. Applied rewrites 79.7%

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

   if -1.10000000000000005e31 < b < 3.4e-5

   1. Initial program 95.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 88.2

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

   5. Applied rewrites 88.2%

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

   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 80.7%

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

Alternative 11: 57.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{1}{\frac{a \cdot y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -4e+30) t_1 (if (<= b 3.4e-5) (/ 1.0 (/ (* a 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 <= -4e+30) {
		tmp = t_1;
	} else if (b <= 3.4e-5) {
		tmp = 1.0 / ((a * 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 <= (-4d+30)) then
        tmp = t_1
    else if (b <= 3.4d-5) then
        tmp = 1.0d0 / ((a * 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 <= -4e+30) {
		tmp = t_1;
	} else if (b <= 3.4e-5) {
		tmp = 1.0 / ((a * 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 <= -4e+30:
		tmp = t_1
	elif b <= 3.4e-5:
		tmp = 1.0 / ((a * 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 <= -4e+30)
		tmp = t_1;
	elseif (b <= 3.4e-5)
		tmp = Float64(1.0 / Float64(Float64(a * 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 <= -4e+30)
		tmp = t_1;
	elseif (b <= 3.4e-5)
		tmp = 1.0 / ((a * 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, -4e+30], t$95$1, If[LessEqual[b, 3.4e-5], N[(1.0 / N[(N[(a * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.0000000000000001e30 or 3.4e-5 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 79.7

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

   5. Applied rewrites 79.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 79.7

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

   7. Applied rewrites 79.7%

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

   if -4.0000000000000001e30 < b < 3.4e-5

   1. Initial program 95.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 65.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 38.9%

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

   13. Applied rewrites 43.6%

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

Alternative 12: 52.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b} \cdot \frac{x}{y}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+27}:\\ \;\;\;\;\frac{1}{\frac{a \cdot y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (- b)) (/ x y))))
   (if (<= b -1.4e+31) t_1 (if (<= b 8e+27) (/ 1.0 (/ (* a y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b) * (x / y);
	double tmp;
	if (b <= -1.4e+31) {
		tmp = t_1;
	} else if (b <= 8e+27) {
		tmp = 1.0 / ((a * 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) * (x / y)
    if (b <= (-1.4d+31)) then
        tmp = t_1
    else if (b <= 8d+27) then
        tmp = 1.0d0 / ((a * 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) * (x / y);
	double tmp;
	if (b <= -1.4e+31) {
		tmp = t_1;
	} else if (b <= 8e+27) {
		tmp = 1.0 / ((a * y) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(-b) * (x / y)
	tmp = 0
	if b <= -1.4e+31:
		tmp = t_1
	elif b <= 8e+27:
		tmp = 1.0 / ((a * y) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(-b)) * Float64(x / y))
	tmp = 0.0
	if (b <= -1.4e+31)
		tmp = t_1;
	elseif (b <= 8e+27)
		tmp = Float64(1.0 / Float64(Float64(a * 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) * (x / y);
	tmp = 0.0;
	if (b <= -1.4e+31)
		tmp = t_1;
	elseif (b <= 8e+27)
		tmp = 1.0 / ((a * 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[Exp[(-b)], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+31], t$95$1, If[LessEqual[b, 8e+27], N[(1.0 / N[(N[(a * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.40000000000000008e31 or 8.0000000000000001e27 < 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 81.0

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

   5. Applied rewrites 81.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 72.2

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

   7. Applied rewrites 72.2%

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

   if -1.40000000000000008e31 < b < 8.0000000000000001e27

   1. Initial program 96.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 87.4

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 64.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 37.8%

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

   13. Applied rewrites 42.3%

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

Alternative 13: 31.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log a \leq -153:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{a \cdot y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (log a) -153.0) (/ (/ x a) 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) <= -153.0) {
		tmp = (x / a) / 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) <= (-153.0d0)) then
        tmp = (x / a) / 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) <= -153.0) {
		tmp = (x / a) / 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) <= -153.0:
		tmp = (x / a) / 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) <= -153.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(-1.0 / Float64(a * y)) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (log(a) <= -153.0)
		tmp = (x / a) / 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], -153.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(-1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 a) < -153

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 80.4

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

   5. Applied rewrites 80.4%

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

   7. Applied rewrites 70.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 70.4%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 37.0%

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

   if -153 < (log.f64 a)

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 67.4

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 27.9%

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

   13. Applied rewrites 34.1%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \leq -153:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{a \cdot y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log a \leq 18:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (log a) 18.0) (/ (/ x a) y) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (log(a) <= 18.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (log(a) <= 18.0d0) then
        tmp = (x / a) / y
    else
        tmp = x / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (Math.log(a) <= 18.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if math.log(a) <= 18.0:
		tmp = (x / a) / y
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (log(a) <= 18.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (log(a) <= 18.0)
		tmp = (x / a) / y;
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[Log[a], $MachinePrecision], 18.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 a) < 18

   1. Initial program 99.5%

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

   7. Applied rewrites 69.6%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 68.3%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 35.0%

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

   if 18 < (log.f64 a)

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 67.7

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

   5. Applied rewrites 67.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 49.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 27.5%

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

   13. Applied rewrites 34.5%

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

Alternative 15: 30.3% accurate, 19.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. 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 72.0

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

5. Applied rewrites 72.0%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 53.4%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 29.6%

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

13. Applied rewrites 32.3%

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

Developer Target 1: 71.5% 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 2024296 
(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))