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

Percentage Accurate: 98.4% → 98.4%

Time: 12.6s

Alternatives: 16

Speedup: 1.0×

• 47.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% 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 98.8%

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

3. Final simplification 98.8%

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

Alternative 2: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -452:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;t\_1 \leq 40000:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (/ (* (pow a (- t 1.0)) x) y)))
   (if (<= t_1 -1e+47)
     t_2
     (if (<= t_1 -452.0)
       (/ x (* (* (exp b) y) a))
       (if (<= t_1 40000.0) (* (/ (pow z y) y) (/ x a)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) * x) / y;
	double tmp;
	if (t_1 <= -1e+47) {
		tmp = t_2;
	} else if (t_1 <= -452.0) {
		tmp = x / ((exp(b) * y) * a);
	} else if (t_1 <= 40000.0) {
		tmp = (pow(z, y) / y) * (x / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) * x) / y
    if (t_1 <= (-1d+47)) then
        tmp = t_2
    else if (t_1 <= (-452.0d0)) then
        tmp = x / ((exp(b) * y) * a)
    else if (t_1 <= 40000.0d0) then
        tmp = ((z ** y) / y) * (x / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) * x) / y;
	double tmp;
	if (t_1 <= -1e+47) {
		tmp = t_2;
	} else if (t_1 <= -452.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else if (t_1 <= 40000.0) {
		tmp = (Math.pow(z, y) / y) * (x / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) * x) / y
	tmp = 0
	if t_1 <= -1e+47:
		tmp = t_2
	elif t_1 <= -452.0:
		tmp = x / ((math.exp(b) * y) * a)
	elif t_1 <= 40000.0:
		tmp = (math.pow(z, y) / y) * (x / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y)
	tmp = 0.0
	if (t_1 <= -1e+47)
		tmp = t_2;
	elseif (t_1 <= -452.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	elseif (t_1 <= 40000.0)
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) * x) / y;
	tmp = 0.0;
	if (t_1 <= -1e+47)
		tmp = t_2;
	elseif (t_1 <= -452.0)
		tmp = x / ((exp(b) * y) * a);
	elseif (t_1 <= 40000.0)
		tmp = ((z ^ y) / y) * (x / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+47], t$95$2, If[LessEqual[t$95$1, -452.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 40000.0], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1e47 or 4e4 < (*.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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 70.6

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.4%

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

   if -1e47 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -452

   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 y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. times-frac N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-exp.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 87.6%

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

   if -452 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4e4

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 66.3

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. exp-to-pow N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. exp-to-pow N/A

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

      11. lower-pow.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-pow.f64 75.8

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

   8. Applied rewrites 75.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 75.9%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq -452:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 40000:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ t_2 := \frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;y \leq 40000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (pow a (- t 1.0)) x) y)) (t_2 (/ (/ (* (pow z y) x) a) y)))
   (if (<= y -7.5e+130)
     t_2
     (if (<= y -6.2e-206)
       t_1
       (if (<= y 8.5e-150)
         (/ (* (exp (- (- (log a)) b)) x) y)
         (if (<= y 40000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, (t - 1.0)) * x) / y;
	double t_2 = ((pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -7.5e+130) {
		tmp = t_2;
	} else if (y <= -6.2e-206) {
		tmp = t_1;
	} else if (y <= 8.5e-150) {
		tmp = (exp((-log(a) - b)) * x) / y;
	} else if (y <= 40000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a ** (t - 1.0d0)) * x) / y
    t_2 = (((z ** y) * x) / a) / y
    if (y <= (-7.5d+130)) then
        tmp = t_2
    else if (y <= (-6.2d-206)) then
        tmp = t_1
    else if (y <= 8.5d-150) then
        tmp = (exp((-log(a) - b)) * x) / y
    else if (y <= 40000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.pow(a, (t - 1.0)) * x) / y;
	double t_2 = ((Math.pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -7.5e+130) {
		tmp = t_2;
	} else if (y <= -6.2e-206) {
		tmp = t_1;
	} else if (y <= 8.5e-150) {
		tmp = (Math.exp((-Math.log(a) - b)) * x) / y;
	} else if (y <= 40000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, (t - 1.0)) * x) / y
	t_2 = ((math.pow(z, y) * x) / a) / y
	tmp = 0
	if y <= -7.5e+130:
		tmp = t_2
	elif y <= -6.2e-206:
		tmp = t_1
	elif y <= 8.5e-150:
		tmp = (math.exp((-math.log(a) - b)) * x) / y
	elif y <= 40000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y)
	t_2 = Float64(Float64(Float64((z ^ y) * x) / a) / y)
	tmp = 0.0
	if (y <= -7.5e+130)
		tmp = t_2;
	elseif (y <= -6.2e-206)
		tmp = t_1;
	elseif (y <= 8.5e-150)
		tmp = Float64(Float64(exp(Float64(Float64(-log(a)) - b)) * x) / y);
	elseif (y <= 40000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ (t - 1.0)) * x) / y;
	t_2 = (((z ^ y) * x) / a) / y;
	tmp = 0.0;
	if (y <= -7.5e+130)
		tmp = t_2;
	elseif (y <= -6.2e-206)
		tmp = t_1;
	elseif (y <= 8.5e-150)
		tmp = (exp((-log(a) - b)) * x) / y;
	elseif (y <= 40000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -7.5e+130], t$95$2, If[LessEqual[y, -6.2e-206], t$95$1, If[LessEqual[y, 8.5e-150], N[(N[(N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 40000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000003e130 or 4e4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.7%

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

   if -7.5000000000000003e130 < y < -6.2000000000000005e-206 or 8.4999999999999997e-150 < y < 4e4

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.3%

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

   if -6.2000000000000005e-206 < y < 8.4999999999999997e-150

   1. Initial program 98.8%

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

   3. 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 98.8

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 82.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-206}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{e^{\left(-\log a\right) - b} \cdot x}{y}\\ \mathbf{elif}\;y \leq 40000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* (pow z y) x) a) y)))
   (if (<= y -7.5e+134)
     t_1
     (if (<= y 9.2e+67) (/ (* (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 = ((pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -7.5e+134) {
		tmp = t_1;
	} else if (y <= 9.2e+67) {
		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 = (((z ** y) * x) / a) / y
    if (y <= (-7.5d+134)) then
        tmp = t_1
    else if (y <= 9.2d+67) 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 = ((Math.pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -7.5e+134) {
		tmp = t_1;
	} else if (y <= 9.2e+67) {
		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 = ((math.pow(z, y) * x) / a) / y
	tmp = 0
	if y <= -7.5e+134:
		tmp = t_1
	elif y <= 9.2e+67:
		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(Float64(Float64((z ^ y) * x) / a) / y)
	tmp = 0.0
	if (y <= -7.5e+134)
		tmp = t_1;
	elseif (y <= 9.2e+67)
		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 = (((z ^ y) * x) / a) / y;
	tmp = 0.0;
	if (y <= -7.5e+134)
		tmp = t_1;
	elseif (y <= 9.2e+67)
		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[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -7.5e+134], t$95$1, If[LessEqual[y, 9.2e+67], 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 < -7.5000000000000001e134 or 9.1999999999999994e67 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 72.7

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.6%

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

   if -7.5000000000000001e134 < y < 9.1999999999999994e67

   1. Initial program 98.1%

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

   3. Taylor expanded in 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 94.3

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

   5. Applied rewrites 94.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1150000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot \left({z}^{y} \cdot x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -4.1e+149)
     t_1
     (if (<= b 1150000.0) (/ (* (pow a (- t 1.0)) (* (pow z y) x)) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -4.1e+149) {
		tmp = t_1;
	} else if (b <= 1150000.0) {
		tmp = (pow(a, (t - 1.0)) * (pow(z, y) * x)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-4.1d+149)) then
        tmp = t_1
    else if (b <= 1150000.0d0) then
        tmp = ((a ** (t - 1.0d0)) * ((z ** y) * x)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -4.1e+149) {
		tmp = t_1;
	} else if (b <= 1150000.0) {
		tmp = (Math.pow(a, (t - 1.0)) * (Math.pow(z, y) * x)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -4.1e+149:
		tmp = t_1
	elif b <= 1150000.0:
		tmp = (math.pow(a, (t - 1.0)) * (math.pow(z, y) * x)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -4.1e+149)
		tmp = t_1;
	elseif (b <= 1150000.0)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * Float64((z ^ y) * x)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -4.1e+149)
		tmp = t_1;
	elseif (b <= 1150000.0)
		tmp = ((a ^ (t - 1.0)) * ((z ^ y) * x)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -4.1e+149], t$95$1, If[LessEqual[b, 1150000.0], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.0999999999999996e149 or 1.15e6 < 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 84.3

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

   5. Applied rewrites 84.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.3

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

   7. Applied rewrites 84.3%

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

   if -4.0999999999999996e149 < b < 1.15e6

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 82.6

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

   5. Applied rewrites 82.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 1150000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot \left({z}^{y} \cdot x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 90000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -4.1e+149)
     t_1
     (if (<= b 90000.0) (* (/ (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(-b) / y) * x;
	double tmp;
	if (b <= -4.1e+149) {
		tmp = t_1;
	} else if (b <= 90000.0) {
		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(-b) / y) * x
    if (b <= (-4.1d+149)) then
        tmp = t_1
    else if (b <= 90000.0d0) 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(-b) / y) * x;
	double tmp;
	if (b <= -4.1e+149) {
		tmp = t_1;
	} else if (b <= 90000.0) {
		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(-b) / y) * x
	tmp = 0
	if b <= -4.1e+149:
		tmp = t_1
	elif b <= 90000.0:
		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(-b)) / y) * x)
	tmp = 0.0
	if (b <= -4.1e+149)
		tmp = t_1;
	elseif (b <= 90000.0)
		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(-b) / y) * x;
	tmp = 0.0;
	if (b <= -4.1e+149)
		tmp = t_1;
	elseif (b <= 90000.0)
		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[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -4.1e+149], t$95$1, If[LessEqual[b, 90000.0], 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 < -4.0999999999999996e149 or 9e4 < 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 84.3

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

   5. Applied rewrites 84.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.3

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

   7. Applied rewrites 84.3%

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

   if -4.0999999999999996e149 < b < 9e4

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 81.6

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

   5. Applied rewrites 81.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 90000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ t_2 := \frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;y \leq 40000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (pow a (- t 1.0)) x) y)) (t_2 (/ (/ (* (pow z y) x) a) y)))
   (if (<= y -7.5e+130)
     t_2
     (if (<= y -3.1e-240)
       t_1
       (if (<= y 8.5e-150)
         (/ x (* (* (exp b) y) a))
         (if (<= y 40000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, (t - 1.0)) * x) / y;
	double t_2 = ((pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -7.5e+130) {
		tmp = t_2;
	} else if (y <= -3.1e-240) {
		tmp = t_1;
	} else if (y <= 8.5e-150) {
		tmp = x / ((exp(b) * y) * a);
	} else if (y <= 40000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a ** (t - 1.0d0)) * x) / y
    t_2 = (((z ** y) * x) / a) / y
    if (y <= (-7.5d+130)) then
        tmp = t_2
    else if (y <= (-3.1d-240)) then
        tmp = t_1
    else if (y <= 8.5d-150) then
        tmp = x / ((exp(b) * y) * a)
    else if (y <= 40000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.pow(a, (t - 1.0)) * x) / y;
	double t_2 = ((Math.pow(z, y) * x) / a) / y;
	double tmp;
	if (y <= -7.5e+130) {
		tmp = t_2;
	} else if (y <= -3.1e-240) {
		tmp = t_1;
	} else if (y <= 8.5e-150) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else if (y <= 40000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, (t - 1.0)) * x) / y
	t_2 = ((math.pow(z, y) * x) / a) / y
	tmp = 0
	if y <= -7.5e+130:
		tmp = t_2
	elif y <= -3.1e-240:
		tmp = t_1
	elif y <= 8.5e-150:
		tmp = x / ((math.exp(b) * y) * a)
	elif y <= 40000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y)
	t_2 = Float64(Float64(Float64((z ^ y) * x) / a) / y)
	tmp = 0.0
	if (y <= -7.5e+130)
		tmp = t_2;
	elseif (y <= -3.1e-240)
		tmp = t_1;
	elseif (y <= 8.5e-150)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	elseif (y <= 40000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a ^ (t - 1.0)) * x) / y;
	t_2 = (((z ^ y) * x) / a) / y;
	tmp = 0.0;
	if (y <= -7.5e+130)
		tmp = t_2;
	elseif (y <= -3.1e-240)
		tmp = t_1;
	elseif (y <= 8.5e-150)
		tmp = x / ((exp(b) * y) * a);
	elseif (y <= 40000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -7.5e+130], t$95$2, If[LessEqual[y, -3.1e-240], t$95$1, If[LessEqual[y, 8.5e-150], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 40000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000003e130 or 4e4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.7%

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

   if -7.5000000000000003e130 < y < -3.10000000000000017e-240 or 8.4999999999999997e-150 < y < 4e4

   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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.5%

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

   if -3.10000000000000017e-240 < y < 8.4999999999999997e-150

   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

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. times-frac N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-exp.f64 72.7

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 78.0%

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

Alternative 8: 58.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -4 \cdot 10^{-10}:\\ \;\;\;\;\frac{t\_1 \cdot x}{y}\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -4e-10)
     (/ (* t_1 x) y)
     (if (<= b -2.15e-131)
       (/ (/ (* (/ x a) (/ x a)) (/ x a)) y)
       (if (<= b 4.4e-13) (/ 1.0 (/ y (/ x a))) (* (/ t_1 y) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double tmp;
	if (b <= -4e-10) {
		tmp = (t_1 * x) / y;
	} else if (b <= -2.15e-131) {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	} else if (b <= 4.4e-13) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = (t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = exp(-b)
    if (b <= (-4d-10)) then
        tmp = (t_1 * x) / y
    else if (b <= (-2.15d-131)) then
        tmp = (((x / a) * (x / a)) / (x / a)) / y
    else if (b <= 4.4d-13) then
        tmp = 1.0d0 / (y / (x / a))
    else
        tmp = (t_1 / 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 t_1 = Math.exp(-b);
	double tmp;
	if (b <= -4e-10) {
		tmp = (t_1 * x) / y;
	} else if (b <= -2.15e-131) {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	} else if (b <= 4.4e-13) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = (t_1 / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(-b)
	tmp = 0
	if b <= -4e-10:
		tmp = (t_1 * x) / y
	elif b <= -2.15e-131:
		tmp = (((x / a) * (x / a)) / (x / a)) / y
	elif b <= 4.4e-13:
		tmp = 1.0 / (y / (x / a))
	else:
		tmp = (t_1 / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -4e-10)
		tmp = Float64(Float64(t_1 * x) / y);
	elseif (b <= -2.15e-131)
		tmp = Float64(Float64(Float64(Float64(x / a) * Float64(x / a)) / Float64(x / a)) / y);
	elseif (b <= 4.4e-13)
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	else
		tmp = Float64(Float64(t_1 / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp(-b);
	tmp = 0.0;
	if (b <= -4e-10)
		tmp = (t_1 * x) / y;
	elseif (b <= -2.15e-131)
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	elseif (b <= 4.4e-13)
		tmp = 1.0 / (y / (x / a));
	else
		tmp = (t_1 / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -4e-10], N[(N[(t$95$1 * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.15e-131], N[(N[(N[(N[(x / a), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] / N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.4e-13], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.00000000000000015e-10

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 70.7

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

   5. Applied rewrites 70.7%

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

   if -4.00000000000000015e-10 < b < -2.15000000000000009e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 18.5%

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

   13. Applied rewrites 46.5%

       \[\leadsto \frac{\frac{0 - \frac{-x}{a} \cdot \frac{-x}{a}}{0 + \frac{-x}{\color{blue}{a}}}}{y} \]

   if -2.15000000000000009e-131 < b < 4.39999999999999993e-13

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 41.8%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 41.8

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

   13. Applied rewrites 41.8%

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

   if 4.39999999999999993e-13 < 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 77.0

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

   5. Applied rewrites 77.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. 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 77.0

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

   7. Applied rewrites 77.0%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-10}:\\ \;\;\;\;\frac{e^{-b} \cdot x}{y}\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -4 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -4e-10)
     t_1
     (if (<= b -2.15e-131)
       (/ (/ (* (/ x a) (/ x a)) (/ x a)) y)
       (if (<= b 4.4e-13) (/ 1.0 (/ y (/ x a))) 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-10) {
		tmp = t_1;
	} else if (b <= -2.15e-131) {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	} else if (b <= 4.4e-13) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-4d-10)) then
        tmp = t_1
    else if (b <= (-2.15d-131)) then
        tmp = (((x / a) * (x / a)) / (x / a)) / y
    else if (b <= 4.4d-13) then
        tmp = 1.0d0 / (y / (x / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -4e-10) {
		tmp = t_1;
	} else if (b <= -2.15e-131) {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	} else if (b <= 4.4e-13) {
		tmp = 1.0 / (y / (x / a));
	} 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-10:
		tmp = t_1
	elif b <= -2.15e-131:
		tmp = (((x / a) * (x / a)) / (x / a)) / y
	elif b <= 4.4e-13:
		tmp = 1.0 / (y / (x / a))
	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-10)
		tmp = t_1;
	elseif (b <= -2.15e-131)
		tmp = Float64(Float64(Float64(Float64(x / a) * Float64(x / a)) / Float64(x / a)) / y);
	elseif (b <= 4.4e-13)
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	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-10)
		tmp = t_1;
	elseif (b <= -2.15e-131)
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	elseif (b <= 4.4e-13)
		tmp = 1.0 / (y / (x / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -4e-10], t$95$1, If[LessEqual[b, -2.15e-131], N[(N[(N[(N[(x / a), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] / N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.4e-13], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.00000000000000015e-10 or 4.39999999999999993e-13 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 74.0

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

   5. Applied rewrites 74.0%

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

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 74.0

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

   7. Applied rewrites 74.0%

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

   if -4.00000000000000015e-10 < b < -2.15000000000000009e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 18.5%

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

   13. Applied rewrites 46.5%

       \[\leadsto \frac{\frac{0 - \frac{-x}{a} \cdot \frac{-x}{a}}{0 + \frac{-x}{\color{blue}{a}}}}{y} \]

   if -2.15000000000000009e-131 < b < 4.39999999999999993e-13

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 41.8%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 41.8

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

   13. Applied rewrites 41.8%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-10}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot e^{-b}\\ \mathbf{if}\;b \leq -4 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x y) (exp (- b)))))
   (if (<= b -4e-10)
     t_1
     (if (<= b -2.15e-131)
       (/ (/ (* (/ x a) (/ x a)) (/ x a)) y)
       (if (<= b 4.4e-13) (/ 1.0 (/ y (/ x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * exp(-b);
	double tmp;
	if (b <= -4e-10) {
		tmp = t_1;
	} else if (b <= -2.15e-131) {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	} else if (b <= 4.4e-13) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * exp(-b)
    if (b <= (-4d-10)) then
        tmp = t_1
    else if (b <= (-2.15d-131)) then
        tmp = (((x / a) * (x / a)) / (x / a)) / y
    else if (b <= 4.4d-13) then
        tmp = 1.0d0 / (y / (x / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * Math.exp(-b);
	double tmp;
	if (b <= -4e-10) {
		tmp = t_1;
	} else if (b <= -2.15e-131) {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	} else if (b <= 4.4e-13) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) * math.exp(-b)
	tmp = 0
	if b <= -4e-10:
		tmp = t_1
	elif b <= -2.15e-131:
		tmp = (((x / a) * (x / a)) / (x / a)) / y
	elif b <= 4.4e-13:
		tmp = 1.0 / (y / (x / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) * exp(Float64(-b)))
	tmp = 0.0
	if (b <= -4e-10)
		tmp = t_1;
	elseif (b <= -2.15e-131)
		tmp = Float64(Float64(Float64(Float64(x / a) * Float64(x / a)) / Float64(x / a)) / y);
	elseif (b <= 4.4e-13)
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) * exp(-b);
	tmp = 0.0;
	if (b <= -4e-10)
		tmp = t_1;
	elseif (b <= -2.15e-131)
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	elseif (b <= 4.4e-13)
		tmp = 1.0 / (y / (x / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e-10], t$95$1, If[LessEqual[b, -2.15e-131], N[(N[(N[(N[(x / a), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] / N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.4e-13], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.00000000000000015e-10 or 4.39999999999999993e-13 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 74.0

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

   5. Applied rewrites 74.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 63.3

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

   7. Applied rewrites 63.3%

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

   if -4.00000000000000015e-10 < b < -2.15000000000000009e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 18.5%

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

   13. Applied rewrites 46.5%

       \[\leadsto \frac{\frac{0 - \frac{-x}{a} \cdot \frac{-x}{a}}{0 + \frac{-x}{\color{blue}{a}}}}{y} \]

   if -2.15000000000000009e-131 < b < 4.39999999999999993e-13

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 41.8%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 41.8

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

   13. Applied rewrites 41.8%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y} \cdot e^{-b}\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-131}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot e^{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 38000000000000:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (pow a (- t 1.0)) x) y)))
   (if (<= t -3e+89)
     t_1
     (if (<= t 38000000000000.0) (/ x (* (* (exp b) y) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(a, (t - 1.0)) * x) / y;
	double tmp;
	if (t <= -3e+89) {
		tmp = t_1;
	} else if (t <= 38000000000000.0) {
		tmp = x / ((exp(b) * y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a ** (t - 1.0d0)) * x) / y
    if (t <= (-3d+89)) then
        tmp = t_1
    else if (t <= 38000000000000.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.pow(a, (t - 1.0)) * x) / y;
	double tmp;
	if (t <= -3e+89) {
		tmp = t_1;
	} else if (t <= 38000000000000.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(a, (t - 1.0)) * x) / y
	tmp = 0
	if t <= -3e+89:
		tmp = t_1
	elif t <= 38000000000000.0:
		tmp = x / ((math.exp(b) * y) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y)
	tmp = 0.0
	if (t <= -3e+89)
		tmp = t_1;
	elseif (t <= 38000000000000.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	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)) * x) / y;
	tmp = 0.0;
	if (t <= -3e+89)
		tmp = t_1;
	elseif (t <= 38000000000000.0)
		tmp = x / ((exp(b) * y) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -3e+89], t$95$1, If[LessEqual[t, 38000000000000.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000013e89 or 3.8e13 < 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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.6%

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

   if -3.00000000000000013e89 < t < 3.8e13

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. times-frac N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-exp.f64 60.4

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

   5. Applied rewrites 60.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.4%

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

Alternative 12: 74.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 32000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.35e+123)
     t_1
     (if (<= b 32000.0) (/ (* (pow a (- t 1.0)) x) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -1.35e+123) {
		tmp = t_1;
	} else if (b <= 32000.0) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-1.35d+123)) then
        tmp = t_1
    else if (b <= 32000.0d0) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -1.35e+123) {
		tmp = t_1;
	} else if (b <= 32000.0) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -1.35e+123:
		tmp = t_1
	elif b <= 32000.0:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -1.35e+123)
		tmp = t_1;
	elseif (b <= 32000.0)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -1.35e+123)
		tmp = t_1;
	elseif (b <= 32000.0)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -1.35e+123], t$95$1, If[LessEqual[b, 32000.0], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35000000000000007e123 or 32000 < 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 84.9

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

   5. Applied rewrites 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.9

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

   7. Applied rewrites 84.9%

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

   if -1.35000000000000007e123 < b < 32000

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.4%

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

Alternative 13: 30.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.7e-9)
   (/ 1.0 (/ y (/ x a)))
   (/ (/ (* (/ x a) (/ x a)) (/ x a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.7e-9) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = (((x / a) * (x / a)) / (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 (y <= 1.7d-9) then
        tmp = 1.0d0 / (y / (x / a))
    else
        tmp = (((x / a) * (x / a)) / (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 (y <= 1.7e-9) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.7e-9:
		tmp = 1.0 / (y / (x / a))
	else:
		tmp = (((x / a) * (x / a)) / (x / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.7e-9)
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(Float64(x / a) * Float64(x / a)) / Float64(x / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.7e-9)
		tmp = 1.0 / (y / (x / a));
	else
		tmp = (((x / a) * (x / a)) / (x / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.7e-9], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / a), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] / N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6999999999999999e-9

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 38.0%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 38.0

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

   13. Applied rewrites 38.0%

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

   if 1.6999999999999999e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 20.2%

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

   13. Applied rewrites 35.7%

       \[\leadsto \frac{\frac{0 - \frac{-x}{a} \cdot \frac{-x}{a}}{0 + \frac{-x}{\color{blue}{a}}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} \cdot \frac{x}{a}}{\frac{x}{a}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.7% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a \cdot x - 0 \cdot a}{a \cdot a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6e-15)
   (/ 1.0 (/ y (/ x a)))
   (/ (/ (- (* a x) (* 0.0 a)) (* a a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6e-15) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = (((a * x) - (0.0 * a)) / (a * 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 (y <= 6d-15) then
        tmp = 1.0d0 / (y / (x / a))
    else
        tmp = (((a * x) - (0.0d0 * a)) / (a * 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 (y <= 6e-15) {
		tmp = 1.0 / (y / (x / a));
	} else {
		tmp = (((a * x) - (0.0 * a)) / (a * a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6e-15:
		tmp = 1.0 / (y / (x / a))
	else:
		tmp = (((a * x) - (0.0 * a)) / (a * a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6e-15)
		tmp = Float64(1.0 / Float64(y / Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(Float64(a * x) - Float64(0.0 * a)) / Float64(a * a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6e-15)
		tmp = 1.0 / (y / (x / a));
	else
		tmp = (((a * x) - (0.0 * a)) / (a * a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6e-15], N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(a * x), $MachinePrecision] - N[(0.0 * a), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6e-15

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 55.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 37.7%

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

       1. lift-/.f64 N/A

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

       2. clear-num N/A

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

       3. lower-/.f64 N/A

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

       4. lower-/.f64 37.7

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

   13. Applied rewrites 37.7%

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

   if 6e-15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 68.9

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

   5. Applied rewrites 68.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 21.3%

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

   13. Applied rewrites 29.0%

       \[\leadsto \frac{\frac{0 \cdot \left(-a\right) - \left(-a\right) \cdot x}{\left(-a\right) \cdot \left(-a\right)}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a \cdot x - 0 \cdot a}{a \cdot a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.6% accurate, 9.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in b around 0

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

   1. exp-sum N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. exp-to-pow N/A

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

   7. lower-pow.f64 N/A

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

   8. exp-prod N/A

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

   9. lower-pow.f64 N/A

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

   10. rem-exp-log N/A

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

   11. lower--.f64 73.2

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

5. Applied rewrites 73.2%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 63.0%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 32.7%

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

    1. lift-/.f64 N/A

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

    2. clear-num N/A

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

    3. lower-/.f64 N/A

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

    4. lower-/.f64 32.7

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

13. Applied rewrites 32.7%

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

Alternative 16: 31.4% accurate, 14.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in b around 0

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

   1. exp-sum N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. exp-to-pow N/A

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

   7. lower-pow.f64 N/A

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

   8. exp-prod N/A

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

   9. lower-pow.f64 N/A

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

   10. rem-exp-log N/A

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

   11. lower--.f64 73.2

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

5. Applied rewrites 73.2%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 63.0%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 32.7%

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

Developer Target 1: 71.9% 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 2024276 
(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))