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

Percentage Accurate: 98.3% → 98.3%

Time: 12.2s

Alternatives: 18

Speedup: 1.0×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

Alternative 2: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_1 \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;t\_1 \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))))
   (if (<= t_1 -5000000000000.0)
     (* x (/ (pow a (- t 1.0)) y))
     (if (<= t_1 580.0)
       (/ x (* (* (exp b) y) a))
       (/ (/ (* (pow a t) x) y) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double tmp;
	if (t_1 <= -5000000000000.0) {
		tmp = x * (pow(a, (t - 1.0)) / y);
	} else if (t_1 <= 580.0) {
		tmp = x / ((exp(b) * y) * a);
	} else {
		tmp = ((pow(a, t) * x) / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    if (t_1 <= (-5000000000000.0d0)) then
        tmp = x * ((a ** (t - 1.0d0)) / y)
    else if (t_1 <= 580.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else
        tmp = (((a ** t) * x) / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double tmp;
	if (t_1 <= -5000000000000.0) {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	} else if (t_1 <= 580.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else {
		tmp = ((Math.pow(a, t) * x) / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	tmp = 0
	if t_1 <= -5000000000000.0:
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	elif t_1 <= 580.0:
		tmp = x / ((math.exp(b) * y) * a)
	else:
		tmp = ((math.pow(a, t) * x) / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_1 <= -5000000000000.0)
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	elseif (t_1 <= 580.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	else
		tmp = Float64(Float64(Float64((a ^ t) * x) / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	tmp = 0.0;
	if (t_1 <= -5000000000000.0)
		tmp = x * ((a ^ (t - 1.0)) / y);
	elseif (t_1 <= 580.0)
		tmp = x / ((exp(b) * y) * a);
	else
		tmp = (((a ^ t) * x) / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000000.0], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 580.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Power[a, t], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e12

   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 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 71.8

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.3%

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

   if -5e12 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 580

   1. Initial program 97.0%

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

   3. Taylor expanded in 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 67.5

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

   5. Applied rewrites 67.5%

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 77.0%

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

   if 580 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.5%

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

   3. Taylor expanded in 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 69.9

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

   5. Applied rewrites 69.9%

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

   7. Applied rewrites 73.4%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 80.4%

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

   12. Applied rewrites 81.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;\left(t - 1\right) \cdot \log a \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_1 \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;t\_1 \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))))
   (if (<= t_1 -5000000000000.0)
     (* x (/ (pow a (- t 1.0)) y))
     (if (<= t_1 580.0)
       (/ x (* (* (exp b) y) a))
       (/ (/ (* (pow a t) x) a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double tmp;
	if (t_1 <= -5000000000000.0) {
		tmp = x * (pow(a, (t - 1.0)) / y);
	} else if (t_1 <= 580.0) {
		tmp = x / ((exp(b) * y) * a);
	} else {
		tmp = ((pow(a, t) * 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) :: t_1
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    if (t_1 <= (-5000000000000.0d0)) then
        tmp = x * ((a ** (t - 1.0d0)) / y)
    else if (t_1 <= 580.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else
        tmp = (((a ** t) * 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 t_1 = (t - 1.0) * Math.log(a);
	double tmp;
	if (t_1 <= -5000000000000.0) {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	} else if (t_1 <= 580.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else {
		tmp = ((Math.pow(a, t) * x) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	tmp = 0
	if t_1 <= -5000000000000.0:
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	elif t_1 <= 580.0:
		tmp = x / ((math.exp(b) * y) * a)
	else:
		tmp = ((math.pow(a, t) * x) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_1 <= -5000000000000.0)
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	elseif (t_1 <= 580.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	else
		tmp = Float64(Float64(Float64((a ^ t) * x) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	tmp = 0.0;
	if (t_1 <= -5000000000000.0)
		tmp = x * ((a ^ (t - 1.0)) / y);
	elseif (t_1 <= 580.0)
		tmp = x / ((exp(b) * y) * a);
	else
		tmp = (((a ^ t) * x) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000000.0], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 580.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Power[a, t], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e12

   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 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 71.8

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.3%

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

   if -5e12 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 580

   1. Initial program 97.0%

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

   3. Taylor expanded in 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 67.5

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

   5. Applied rewrites 67.5%

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 77.0%

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

   if 580 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.5%

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

   3. Taylor expanded in 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 69.9

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

   5. Applied rewrites 69.9%

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

   7. Applied rewrites 73.4%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 80.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;\left(t - 1\right) \cdot \log a \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_2 \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;t\_2 \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t\_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0))) (t_2 (* (- t 1.0) (log a))))
   (if (<= t_2 -5000000000000.0)
     (* x (/ t_1 y))
     (if (<= t_2 580.0) (/ x (* (* (exp b) y) a)) (/ (* x t_1) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (t - 1.0) * log(a);
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = x * (t_1 / y);
	} else if (t_2 <= 580.0) {
		tmp = x / ((exp(b) * y) * a);
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (t - 1.0d0) * log(a)
    if (t_2 <= (-5000000000000.0d0)) then
        tmp = x * (t_1 / y)
    else if (t_2 <= 580.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else
        tmp = (x * t_1) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (t - 1.0) * Math.log(a);
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = x * (t_1 / y);
	} else if (t_2 <= 580.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (t - 1.0) * math.log(a)
	tmp = 0
	if t_2 <= -5000000000000.0:
		tmp = x * (t_1 / y)
	elif t_2 <= 580.0:
		tmp = x / ((math.exp(b) * y) * a)
	else:
		tmp = (x * t_1) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_2 <= -5000000000000.0)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (t_2 <= 580.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	else
		tmp = Float64(Float64(x * t_1) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (t - 1.0) * log(a);
	tmp = 0.0;
	if (t_2 <= -5000000000000.0)
		tmp = x * (t_1 / y);
	elseif (t_2 <= 580.0)
		tmp = x / ((exp(b) * y) * a);
	else
		tmp = (x * t_1) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5000000000000.0], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 580.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e12

   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 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 71.8

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.3%

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

   if -5e12 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 580

   1. Initial program 97.0%

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

   3. Taylor expanded in 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 67.5

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

   5. Applied rewrites 67.5%

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 77.0%

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

   if 580 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.5%

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

   3. Taylor expanded in 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 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 80.6

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

   8. Applied rewrites 80.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 80.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;\left(t - 1\right) \cdot \log a \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \left(t - 1\right) \cdot \log a\\ \mathbf{if}\;t\_2 \leq -5000000000000:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;t\_2 \leq 580:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot a\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t\_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0))) (t_2 (* (- t 1.0) (log a))))
   (if (<= t_2 -5000000000000.0)
     (* x (/ t_1 y))
     (if (<= t_2 580.0) (/ x (* (* (exp b) a) y)) (/ (* x t_1) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (t - 1.0) * log(a);
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = x * (t_1 / y);
	} else if (t_2 <= 580.0) {
		tmp = x / ((exp(b) * a) * y);
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (t - 1.0d0) * log(a)
    if (t_2 <= (-5000000000000.0d0)) then
        tmp = x * (t_1 / y)
    else if (t_2 <= 580.0d0) then
        tmp = x / ((exp(b) * a) * y)
    else
        tmp = (x * t_1) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (t - 1.0) * Math.log(a);
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = x * (t_1 / y);
	} else if (t_2 <= 580.0) {
		tmp = x / ((Math.exp(b) * a) * y);
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (t - 1.0) * math.log(a)
	tmp = 0
	if t_2 <= -5000000000000.0:
		tmp = x * (t_1 / y)
	elif t_2 <= 580.0:
		tmp = x / ((math.exp(b) * a) * y)
	else:
		tmp = (x * t_1) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(t - 1.0) * log(a))
	tmp = 0.0
	if (t_2 <= -5000000000000.0)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (t_2 <= 580.0)
		tmp = Float64(x / Float64(Float64(exp(b) * a) * y));
	else
		tmp = Float64(Float64(x * t_1) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (t - 1.0) * log(a);
	tmp = 0.0;
	if (t_2 <= -5000000000000.0)
		tmp = x * (t_1 / y);
	elseif (t_2 <= 580.0)
		tmp = x / ((exp(b) * a) * y);
	else
		tmp = (x * t_1) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5000000000000.0], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 580.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e12

   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 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 71.8

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.3%

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

   if -5e12 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 580

   1. Initial program 97.0%

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

   3. Taylor expanded in 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 67.5

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

   5. Applied rewrites 67.5%

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

   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 76.9%

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

   if 580 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.5%

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

   3. Taylor expanded in 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 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 80.6

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

   8. Applied rewrites 80.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 80.4%

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

Alternative 6: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+37} \lor \neg \left(y \leq 3.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e+37) (not (<= y 3.7e+21)))
   (/ (* x (exp (- (fma (log z) y (- (log a))) b))) y)
   (/ (* x (exp (- (* (- t 1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+37) || !(y <= 3.7e+21)) {
		tmp = (x * exp((fma(log(z), y, -log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e+37) || !(y <= 3.7e+21))
		tmp = Float64(Float64(x * exp(Float64(fma(log(z), y, Float64(-log(a))) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t - 1.0) * log(a)) - b))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e+37], N[Not[LessEqual[y, 3.7e+21]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000011e37 or 3.7e21 < 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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 95.5

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

   5. Applied rewrites 95.5%

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

   if -1.50000000000000011e37 < y < 3.7e21

   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 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 96.2

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

   5. Applied rewrites 96.2%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+37} \lor \neg \left(y \leq 3.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{-1}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) t) b))) y)))
   (if (<= b -5.1e+19)
     t_1
     (if (<= b -3.1e-171)
       (/ (* x (pow a (- t 1.0))) y)
       (if (<= b 1.16e-43) (/ (* x (* (pow z y) (pow a -1.0))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * t) - b))) / y;
	double tmp;
	if (b <= -5.1e+19) {
		tmp = t_1;
	} else if (b <= -3.1e-171) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else if (b <= 1.16e-43) {
		tmp = (x * (pow(z, y) * pow(a, -1.0))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((log(a) * t) - b))) / y
    if (b <= (-5.1d+19)) then
        tmp = t_1
    else if (b <= (-3.1d-171)) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else if (b <= 1.16d-43) then
        tmp = (x * ((z ** y) * (a ** (-1.0d0)))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	double tmp;
	if (b <= -5.1e+19) {
		tmp = t_1;
	} else if (b <= -3.1e-171) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else if (b <= 1.16e-43) {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, -1.0))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((math.log(a) * t) - b))) / y
	tmp = 0
	if b <= -5.1e+19:
		tmp = t_1
	elif b <= -3.1e-171:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	elif b <= 1.16e-43:
		tmp = (x * (math.pow(z, y) * math.pow(a, -1.0))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y)
	tmp = 0.0
	if (b <= -5.1e+19)
		tmp = t_1;
	elseif (b <= -3.1e-171)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	elseif (b <= 1.16e-43)
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ -1.0))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((log(a) * t) - b))) / y;
	tmp = 0.0;
	if (b <= -5.1e+19)
		tmp = t_1;
	elseif (b <= -3.1e-171)
		tmp = (x * (a ^ (t - 1.0))) / y;
	elseif (b <= 1.16e-43)
		tmp = (x * ((z ^ y) * (a ^ -1.0))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -5.1e+19], t$95$1, If[LessEqual[b, -3.1e-171], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.16e-43], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.1e19 or 1.1600000000000001e-43 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 92.1

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

   5. Applied rewrites 92.1%

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

   if -5.1e19 < b < -3.1e-171

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 84.5

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 88.2%

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

   if -3.1e-171 < b < 1.1600000000000001e-43

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 63.3

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

   5. Applied rewrites 63.3%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.1

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 78.0%

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

Alternative 8: 74.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+20}:\\ \;\;\;\;\frac{t\_1}{y} \cdot x\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{-1}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{t\_1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -1.15e+20)
     (* (/ t_1 y) x)
     (if (<= b -3.1e-171)
       (/ (* x (pow a (- t 1.0))) y)
       (if (<= b 7.5e+30)
         (/ (* x (* (pow z y) (pow a -1.0))) y)
         (/ (* x (/ t_1 a)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double tmp;
	if (b <= -1.15e+20) {
		tmp = (t_1 / y) * x;
	} else if (b <= -3.1e-171) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else if (b <= 7.5e+30) {
		tmp = (x * (pow(z, y) * pow(a, -1.0))) / y;
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp(-b)
    if (b <= (-1.15d+20)) then
        tmp = (t_1 / y) * x
    else if (b <= (-3.1d-171)) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else if (b <= 7.5d+30) then
        tmp = (x * ((z ** y) * (a ** (-1.0d0)))) / y
    else
        tmp = (x * (t_1 / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.exp(-b);
	double tmp;
	if (b <= -1.15e+20) {
		tmp = (t_1 / y) * x;
	} else if (b <= -3.1e-171) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else if (b <= 7.5e+30) {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, -1.0))) / y;
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(-b)
	tmp = 0
	if b <= -1.15e+20:
		tmp = (t_1 / y) * x
	elif b <= -3.1e-171:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	elif b <= 7.5e+30:
		tmp = (x * (math.pow(z, y) * math.pow(a, -1.0))) / y
	else:
		tmp = (x * (t_1 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -1.15e+20)
		tmp = Float64(Float64(t_1 / y) * x);
	elseif (b <= -3.1e-171)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	elseif (b <= 7.5e+30)
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ -1.0))) / y);
	else
		tmp = Float64(Float64(x * Float64(t_1 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp(-b);
	tmp = 0.0;
	if (b <= -1.15e+20)
		tmp = (t_1 / y) * x;
	elseif (b <= -3.1e-171)
		tmp = (x * (a ^ (t - 1.0))) / y;
	elseif (b <= 7.5e+30)
		tmp = (x * ((z ^ y) * (a ^ -1.0))) / y;
	else
		tmp = (x * (t_1 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -1.15e+20], N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -3.1e-171], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.5e+30], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e20

   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 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 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 80.0

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

   8. Applied rewrites 80.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.0

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

   10. Applied rewrites 80.0%

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

   if -1.15e20 < b < -3.1e-171

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 84.5

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 88.2%

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

   if -3.1e-171 < b < 7.49999999999999973e30

   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

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   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 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.7

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 76.9%

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

   if 7.49999999999999973e30 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 79.0

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 91.4%

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

Alternative 9: 88.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log z \cdot y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.35e+101)
   (/ (* x (/ (pow z y) a)) y)
   (if (<= y 1.12e+35)
     (/ (* x (exp (- (* (- t 1.0) (log a)) b))) y)
     (/ (* x (exp (* (log z) y))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.35e+101) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (y <= 1.12e+35) {
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((log(z) * y))) / 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 <= (-2.35d+101)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (y <= 1.12d+35) then
        tmp = (x * exp((((t - 1.0d0) * log(a)) - b))) / y
    else
        tmp = (x * exp((log(z) * y))) / 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 <= -2.35e+101) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (y <= 1.12e+35) {
		tmp = (x * Math.exp((((t - 1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((Math.log(z) * y))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.35e+101:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif y <= 1.12e+35:
		tmp = (x * math.exp((((t - 1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((math.log(z) * y))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.35e+101)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (y <= 1.12e+35)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t - 1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(log(z) * y))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.35e+101)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (y <= 1.12e+35)
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((log(z) * y))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.35e+101], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.12e+35], N[(N[(x * N[Exp[N[(N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999985e101

   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 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 56.7

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

   5. Applied rewrites 56.7%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 80.6

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

   8. Applied rewrites 80.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 91.8%

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

   if -2.34999999999999985e101 < y < 1.12000000000000003e35

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 94.1

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

   5. Applied rewrites 94.1%

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

   if 1.12000000000000003e35 < 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 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 67.4

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 88.5

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

   8. Applied rewrites 88.5%

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

Alternative 10: 86.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+19} \lor \neg \left(b \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.5e+19) (not (<= b 7.5e+30)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* (* x (pow z y)) (pow a (- t 1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e+19) || !(b <= 7.5e+30)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = ((x * pow(z, y)) * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.5d+19)) .or. (.not. (b <= 7.5d+30))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = ((x * (z ** y)) * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e+19) || !(b <= 7.5e+30)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = ((x * Math.pow(z, y)) * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.5e+19) or not (b <= 7.5e+30):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = ((x * math.pow(z, y)) * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.5e+19) || !(b <= 7.5e+30))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(Float64(x * (z ^ y)) * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.5e+19) || ~((b <= 7.5e+30)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = ((x * (z ^ y)) * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.5e+19], N[Not[LessEqual[b, 7.5e+30]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.5e19 or 7.49999999999999973e30 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 94.9

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

   5. Applied rewrites 94.9%

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

   if -8.5e19 < b < 7.49999999999999973e30

   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 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 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 22.3

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

   8. Applied rewrites 22.3%

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

   9. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   10. 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. *-commutative N/A

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

       3. exp-to-pow N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 N/A

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

       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-to-pow N/A

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

       9. lower-pow.f64 N/A

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

       10. lower--.f64 89.7

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

   11. Applied rewrites 89.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+19} \lor \neg \left(b \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+19} \lor \neg \left(b \leq 4.7 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.5e+19) (not (<= b 4.7e+27)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (* (* x (pow z y)) (/ (pow a (- t 1.0)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e+19) || !(b <= 4.7e+27)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * pow(z, y)) * (pow(a, (t - 1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.5d+19)) .or. (.not. (b <= 4.7d+27))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * (z ** y)) * ((a ** (t - 1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.5e+19) || !(b <= 4.7e+27)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * Math.pow(z, y)) * (Math.pow(a, (t - 1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.5e+19) or not (b <= 4.7e+27):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * math.pow(z, y)) * (math.pow(a, (t - 1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.5e+19) || !(b <= 4.7e+27))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) * Float64((a ^ Float64(t - 1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.5e+19) || ~((b <= 4.7e+27)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * (z ^ y)) * ((a ^ (t - 1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.5e+19], N[Not[LessEqual[b, 4.7e+27]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.5e19 or 4.69999999999999976e27 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 94.2

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

   5. Applied rewrites 94.2%

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

   if -8.5e19 < b < 4.69999999999999976e27

   1. Initial program 97.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 84.6

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

   5. Applied rewrites 84.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+19} \lor \neg \left(b \leq 4.7 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+20}:\\ \;\;\;\;\frac{t\_1}{y} \cdot x\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{t\_1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -1.15e+20)
     (* (/ t_1 y) x)
     (if (<= b -3.1e-171)
       (/ (* x (pow a (- t 1.0))) y)
       (if (<= b 7.5e+30)
         (/ (* x (/ (pow z y) a)) y)
         (/ (* x (/ t_1 a)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double tmp;
	if (b <= -1.15e+20) {
		tmp = (t_1 / y) * x;
	} else if (b <= -3.1e-171) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else if (b <= 7.5e+30) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp(-b)
    if (b <= (-1.15d+20)) then
        tmp = (t_1 / y) * x
    else if (b <= (-3.1d-171)) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else if (b <= 7.5d+30) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * (t_1 / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.exp(-b);
	double tmp;
	if (b <= -1.15e+20) {
		tmp = (t_1 / y) * x;
	} else if (b <= -3.1e-171) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else if (b <= 7.5e+30) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(-b)
	tmp = 0
	if b <= -1.15e+20:
		tmp = (t_1 / y) * x
	elif b <= -3.1e-171:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	elif b <= 7.5e+30:
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * (t_1 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -1.15e+20)
		tmp = Float64(Float64(t_1 / y) * x);
	elseif (b <= -3.1e-171)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	elseif (b <= 7.5e+30)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64(t_1 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp(-b);
	tmp = 0.0;
	if (b <= -1.15e+20)
		tmp = (t_1 / y) * x;
	elseif (b <= -3.1e-171)
		tmp = (x * (a ^ (t - 1.0))) / y;
	elseif (b <= 7.5e+30)
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * (t_1 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -1.15e+20], N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -3.1e-171], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.5e+30], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e20

   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 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 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 80.0

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

   8. Applied rewrites 80.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.0

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

   10. Applied rewrites 80.0%

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

   if -1.15e20 < b < -3.1e-171

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 84.5

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 88.2%

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

   if -3.1e-171 < b < 7.49999999999999973e30

   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

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   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 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.7

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 76.9%

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

   if 7.49999999999999973e30 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 79.0

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 91.4%

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

Alternative 13: 74.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.15e+20)
     t_1
     (if (<= b -3.1e-171)
       (/ (* x (pow a (- t 1.0))) y)
       (if (<= b 7.5e+30) (/ (* x (/ (pow z y) a)) 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 <= -1.15e+20) {
		tmp = t_1;
	} else if (b <= -3.1e-171) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else if (b <= 7.5e+30) {
		tmp = (x * (pow(z, y) / a)) / 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 <= (-1.15d+20)) then
        tmp = t_1
    else if (b <= (-3.1d-171)) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else if (b <= 7.5d+30) then
        tmp = (x * ((z ** y) / a)) / 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 <= -1.15e+20) {
		tmp = t_1;
	} else if (b <= -3.1e-171) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else if (b <= 7.5e+30) {
		tmp = (x * (Math.pow(z, y) / a)) / 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 <= -1.15e+20:
		tmp = t_1
	elif b <= -3.1e-171:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	elif b <= 7.5e+30:
		tmp = (x * (math.pow(z, y) / a)) / 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 <= -1.15e+20)
		tmp = t_1;
	elseif (b <= -3.1e-171)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	elseif (b <= 7.5e+30)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / 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 <= -1.15e+20)
		tmp = t_1;
	elseif (b <= -3.1e-171)
		tmp = (x * (a ^ (t - 1.0))) / y;
	elseif (b <= 7.5e+30)
		tmp = (x * ((z ^ y) / a)) / 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, -1.15e+20], t$95$1, If[LessEqual[b, -3.1e-171], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.5e+30], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e20 or 7.49999999999999973e30 < 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 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 94.9

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 85.6

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

   8. Applied rewrites 85.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   9. 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 85.6

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

   10. Applied rewrites 85.6%

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

   if -1.15e20 < b < -3.1e-171

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 84.5

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 88.2%

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

   if -3.1e-171 < b < 7.49999999999999973e30

   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

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   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 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.7

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 76.9%

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

Alternative 14: 74.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+20} \lor \neg \left(b \leq 115000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.15e+20) (not (<= b 115000.0)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (pow a (- t 1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e+20) || !(b <= 115000.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.15d+20)) .or. (.not. (b <= 115000.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e+20) || !(b <= 115000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.15e+20) or not (b <= 115000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.15e+20) || !(b <= 115000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.15e+20) || ~((b <= 115000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.15e+20], N[Not[LessEqual[b, 115000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e20 or 115000 < 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 y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 93.5

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

   5. Applied rewrites 93.5%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 84.7

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

   8. Applied rewrites 84.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   9. 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 84.7

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

   10. Applied rewrites 84.7%

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

   if -1.15e20 < b < 115000

   1. Initial program 97.1%

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

   3. Taylor expanded in 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 72.6

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   7. 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. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 89.2

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

   8. Applied rewrites 89.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 74.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+20} \lor \neg \left(b \leq 115000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+114} \lor \neg \left(b \leq 300000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e+114) (not (<= b 300000.0)))
   (* (/ (exp (- b)) y) x)
   (* x (/ (pow a (- t 1.0)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+114) || !(b <= 300000.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = x * (pow(a, (t - 1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.5d+114)) .or. (.not. (b <= 300000.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = x * ((a ** (t - 1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+114) || !(b <= 300000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.5e+114) or not (b <= 300000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.5e+114) || !(b <= 300000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.5e+114) || ~((b <= 300000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = x * ((a ^ (t - 1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.5e+114], N[Not[LessEqual[b, 300000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000001e114 or 3e5 < 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 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%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 88.5

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

   8. Applied rewrites 88.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   9. 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 88.5

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

   10. Applied rewrites 88.5%

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

   if -5.5000000000000001e114 < b < 3e5

   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 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 69.5

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

   5. Applied rewrites 69.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+114} \lor \neg \left(b \leq 300000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+19} \lor \neg \left(b \leq 1.72 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.1e+19) (not (<= b 1.72e-6)))
   (* (/ (exp (- b)) y) x)
   (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.1e+19) || !(b <= 1.72e-6)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.1d+19)) .or. (.not. (b <= 1.72d-6))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.1e+19) || !(b <= 1.72e-6)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.1e+19) or not (b <= 1.72e-6):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.1e+19) || !(b <= 1.72e-6))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.1e+19) || ~((b <= 1.72e-6)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.1e+19], N[Not[LessEqual[b, 1.72e-6]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.1e19 or 1.72e-6 < 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 y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 93.6

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 83.6

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

   8. Applied rewrites 83.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   9. 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 83.6

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

   10. Applied rewrites 83.6%

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

   if -5.1e19 < b < 1.72e-6

   1. Initial program 97.2%

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

   3. Taylor expanded in 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 71.0

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

   5. Applied rewrites 71.0%

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

   7. Applied rewrites 73.0%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 73.6%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 37.4%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+19} \lor \neg \left(b \leq 1.72 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log a \leq -130:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (log a) -130.0) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (log(a) <= -130.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (log(a) <= (-130.0d0)) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (Math.log(a) <= -130.0) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if math.log(a) <= -130.0:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (log(a) <= -130.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (log(a) <= -130.0)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[Log[a], $MachinePrecision], -130.0], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 a) < -130

   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 61.5

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

   5. Applied rewrites 61.5%

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

   7. Applied rewrites 68.6%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 61.3%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 34.0%

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

   if -130 < (log.f64 a)

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   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 74.5

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

   5. Applied rewrites 74.5%

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 59.1%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 30.3%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \leq -130:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.6% accurate, 19.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

3. Taylor expanded in 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 69.3

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

5. Applied rewrites 69.3%

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

7. Applied rewrites 71.0%

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

8. Taylor expanded in b around 0

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

10. Applied rewrites 60.0%

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

11. Taylor expanded in t around 0

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

13. Applied rewrites 28.0%

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

14. Final simplification 28.0%

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

Developer Target 1: 72.0% 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 2024324 
(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))