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

Percentage Accurate: 98.5% → 98.5%

Time: 22.4s

Alternatives: 17

Speedup: 1.0×

• 47.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% 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: 98.5% 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 98.3%

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

2. Final simplification 98.3%

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

Alternative 2: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1.00001 \lor \neg \left(t + -1 \leq 5 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1.00001) (not (<= (+ t -1.0) 5e+23)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1.00001) || !((t + -1.0) <= 5e+23)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 (((t + (-1.0d0)) <= (-1.00001d0)) .or. (.not. ((t + (-1.0d0)) <= 5d+23))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 (((t + -1.0) <= -1.00001) || !((t + -1.0) <= 5e+23)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1.00001) or not ((t + -1.0) <= 5e+23):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1.00001) || !(Float64(t + -1.0) <= 5e+23))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1.00001) || ~(((t + -1.0) <= 5e+23)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1.00001], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 5e+23]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -1.0000100000000001 or 4.9999999999999999e23 < (-.f64 t 1)

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 95.7%

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

   if -1.0000100000000001 < (-.f64 t 1) < 4.9999999999999999e23

   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. Taylor expanded in t around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. mul-1-neg 97.0%

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

      3. unsub-neg 97.0%

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

   4. Simplified 97.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1.00001 \lor \neg \left(t + -1 \leq 5 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 77.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 0.00115:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot {a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -1.25e-10)
     t_1
     (if (<= t 2.3e-161)
       (* (/ x a) (/ (pow z y) (* y (exp b))))
       (if (<= t 0.00115) (/ x (/ y (* (pow z y) (pow a (+ t -1.0))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -1.25e-10) {
		tmp = t_1;
	} else if (t <= 2.3e-161) {
		tmp = (x / a) * (pow(z, y) / (y * exp(b)));
	} else if (t <= 0.00115) {
		tmp = x / (y / (pow(z, y) * pow(a, (t + -1.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((a ** t) / a)) / y
    if (t <= (-1.25d-10)) then
        tmp = t_1
    else if (t <= 2.3d-161) then
        tmp = (x / a) * ((z ** y) / (y * exp(b)))
    else if (t <= 0.00115d0) then
        tmp = x / (y / ((z ** y) * (a ** (t + (-1.0d0)))))
    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.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -1.25e-10) {
		tmp = t_1;
	} else if (t <= 2.3e-161) {
		tmp = (x / a) * (Math.pow(z, y) / (y * Math.exp(b)));
	} else if (t <= 0.00115) {
		tmp = x / (y / (Math.pow(z, y) * Math.pow(a, (t + -1.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -1.25e-10:
		tmp = t_1
	elif t <= 2.3e-161:
		tmp = (x / a) * (math.pow(z, y) / (y * math.exp(b)))
	elif t <= 0.00115:
		tmp = x / (y / (math.pow(z, y) * math.pow(a, (t + -1.0))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -1.25e-10)
		tmp = t_1;
	elseif (t <= 2.3e-161)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / Float64(y * exp(b))));
	elseif (t <= 0.00115)
		tmp = Float64(x / Float64(y / Float64((z ^ y) * (a ^ Float64(t + -1.0)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -1.25e-10)
		tmp = t_1;
	elseif (t <= 2.3e-161)
		tmp = (x / a) * ((z ^ y) / (y * exp(b)));
	elseif (t <= 0.00115)
		tmp = x / (y / ((z ^ y) * (a ^ (t + -1.0))));
	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[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.25e-10], t$95$1, If[LessEqual[t, 2.3e-161], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00115], N[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000008e-10 or 0.00115 < t

   1. Initial program 99.8%

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

      1. associate-*l/ 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-diff 66.1%

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

      4. exp-sum 54.0%

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

      5. *-commutative 54.0%

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

      6. exp-to-pow 54.0%

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

      7. *-commutative 54.0%

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

      8. exp-to-pow 54.0%

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

      9. sub-neg 54.0%

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

      10. metadata-eval 54.0%

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

   3. Simplified 54.0%

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

   4. Taylor expanded in y around 0 74.0%

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

      1. exp-to-pow 74.1%

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

      2. sub-neg 74.1%

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

      3. metadata-eval 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in b around 0 88.0%

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

      1. unpow-prod-up 88.1%

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

      2. unpow-1 88.1%

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

   9. Applied egg-rr 88.1%

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

       1. associate-*r/ 88.1%

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

       2. *-rgt-identity 88.1%

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

   11. Simplified 88.1%

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

   if -1.25000000000000008e-10 < t < 2.3e-161

   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. Step-by-step derivation

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

      3. exp-diff 80.5%

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

      4. exp-sum 80.5%

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

      5. *-commutative 80.5%

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

      6. exp-to-pow 80.5%

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

      7. *-commutative 80.5%

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

      8. exp-to-pow 81.7%

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

      9. sub-neg 81.7%

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

      10. metadata-eval 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. times-frac 87.2%

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

   6. Simplified 87.2%

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

   if 2.3e-161 < t < 0.00115

   1. Initial program 95.0%

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

      1. associate-*l/ 74.5%

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

      2. *-commutative 74.5%

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

      3. exp-diff 54.5%

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

      4. exp-sum 54.7%

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

      5. *-commutative 54.7%

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

      6. exp-to-pow 54.7%

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

      7. *-commutative 54.7%

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

      8. exp-to-pow 56.6%

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

      9. sub-neg 56.6%

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

      10. metadata-eval 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in b around 0 82.1%

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

      1. associate-/l* 85.0%

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

      2. *-commutative 85.0%

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

      3. exp-to-pow 86.5%

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

      4. sub-neg 86.5%

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

      5. metadata-eval 86.5%

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

   6. Simplified 86.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 0.00115:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot {a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 4: 89.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+44} \lor \neg \left(y \leq 10^{+108}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.2e+44) (not (<= y 1e+108)))
   (/ (* x (/ (pow z y) a)) 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 <= -7.2e+44) || !(y <= 1e+108)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / 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 <= (-7.2d+44)) .or. (.not. (y <= 1d+108))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / 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 <= -7.2e+44) || !(y <= 1e+108)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.2e+44) or not (y <= 1e+108):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.2e+44) || !(y <= 1e+108))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.2e+44) || ~((y <= 1e+108)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.2e+44], N[Not[LessEqual[y, 1e+108]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $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 < -7.2e44 or 1e108 < 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. Taylor expanded in t around 0 95.9%

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

      1. +-commutative 95.9%

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

      2. mul-1-neg 95.9%

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

      3. unsub-neg 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in b around 0 91.8%

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

      1. div-exp 91.8%

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

      2. *-commutative 91.8%

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

      3. exp-to-pow 91.8%

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

      4. rem-exp-log 91.8%

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

   7. Simplified 91.8%

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

   if -7.2e44 < y < 1e108

   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. Taylor expanded in y around 0 95.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+44} \lor \neg \left(y \leq 10^{+108}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 77.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -1.25e-10)
     t_1
     (if (<= t 2.2e-271)
       (* (/ x a) (/ (pow z y) (* y (exp b))))
       (if (<= t 6.5e-5) (/ (* 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 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -1.25e-10) {
		tmp = t_1;
	} else if (t <= 2.2e-271) {
		tmp = (x / a) * (pow(z, y) / (y * exp(b)));
	} else if (t <= 6.5e-5) {
		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 = (x * ((a ** t) / a)) / y
    if (t <= (-1.25d-10)) then
        tmp = t_1
    else if (t <= 2.2d-271) then
        tmp = (x / a) * ((z ** y) / (y * exp(b)))
    else if (t <= 6.5d-5) 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 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -1.25e-10) {
		tmp = t_1;
	} else if (t <= 2.2e-271) {
		tmp = (x / a) * (Math.pow(z, y) / (y * Math.exp(b)));
	} else if (t <= 6.5e-5) {
		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 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -1.25e-10:
		tmp = t_1
	elif t <= 2.2e-271:
		tmp = (x / a) * (math.pow(z, y) / (y * math.exp(b)))
	elif t <= 6.5e-5:
		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(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -1.25e-10)
		tmp = t_1;
	elseif (t <= 2.2e-271)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / Float64(y * exp(b))));
	elseif (t <= 6.5e-5)
		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 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -1.25e-10)
		tmp = t_1;
	elseif (t <= 2.2e-271)
		tmp = (x / a) * ((z ^ y) / (y * exp(b)));
	elseif (t <= 6.5e-5)
		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[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.25e-10], t$95$1, If[LessEqual[t, 2.2e-271], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-5], 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 t < -1.25000000000000008e-10 or 6.49999999999999943e-5 < t

   1. Initial program 99.8%

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

      1. associate-*l/ 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-diff 66.1%

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

      4. exp-sum 54.0%

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

      5. *-commutative 54.0%

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

      6. exp-to-pow 54.0%

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

      7. *-commutative 54.0%

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

      8. exp-to-pow 54.0%

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

      9. sub-neg 54.0%

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

      10. metadata-eval 54.0%

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

   3. Simplified 54.0%

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

   4. Taylor expanded in y around 0 74.0%

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

      1. exp-to-pow 74.1%

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

      2. sub-neg 74.1%

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

      3. metadata-eval 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in b around 0 88.0%

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

      1. unpow-prod-up 88.1%

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

      2. unpow-1 88.1%

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

   9. Applied egg-rr 88.1%

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

       1. associate-*r/ 88.1%

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

       2. *-rgt-identity 88.1%

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

   11. Simplified 88.1%

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

   if -1.25000000000000008e-10 < t < 2.1999999999999999e-271

   1. Initial program 96.8%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. exp-diff 82.1%

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

      4. exp-sum 82.1%

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

      5. *-commutative 82.1%

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

      6. exp-to-pow 82.1%

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

      7. *-commutative 82.1%

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

      8. exp-to-pow 83.2%

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

      9. sub-neg 83.2%

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

      10. metadata-eval 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around 0 87.4%

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

      1. times-frac 87.4%

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

   6. Simplified 87.4%

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

   if 2.1999999999999999e-271 < t < 6.49999999999999943e-5

   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. Taylor expanded in t around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. mul-1-neg 97.0%

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

      3. unsub-neg 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in b around 0 85.0%

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

      1. div-exp 85.1%

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

      2. *-commutative 85.1%

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

      3. exp-to-pow 85.1%

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

      4. rem-exp-log 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 6: 75.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 0.00105:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -9e+33)
     t_1
     (if (<= t 1.45e-292)
       (/ x (* a (* y (exp b))))
       (if (<= t 0.00105) (/ (* 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 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -9e+33) {
		tmp = t_1;
	} else if (t <= 1.45e-292) {
		tmp = x / (a * (y * exp(b)));
	} else if (t <= 0.00105) {
		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 = (x * ((a ** t) / a)) / y
    if (t <= (-9d+33)) then
        tmp = t_1
    else if (t <= 1.45d-292) then
        tmp = x / (a * (y * exp(b)))
    else if (t <= 0.00105d0) 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 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -9e+33) {
		tmp = t_1;
	} else if (t <= 1.45e-292) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t <= 0.00105) {
		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 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -9e+33:
		tmp = t_1
	elif t <= 1.45e-292:
		tmp = x / (a * (y * math.exp(b)))
	elif t <= 0.00105:
		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(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -9e+33)
		tmp = t_1;
	elseif (t <= 1.45e-292)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t <= 0.00105)
		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 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -9e+33)
		tmp = t_1;
	elseif (t <= 1.45e-292)
		tmp = x / (a * (y * exp(b)));
	elseif (t <= 0.00105)
		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[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -9e+33], t$95$1, If[LessEqual[t, 1.45e-292], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00105], 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 t < -9.0000000000000001e33 or 0.00104999999999999994 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. exp-diff 66.7%

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

      4. exp-sum 54.4%

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

      5. *-commutative 54.4%

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

      6. exp-to-pow 54.4%

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

      7. *-commutative 54.4%

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

      8. exp-to-pow 54.4%

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

      9. sub-neg 54.4%

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

      10. metadata-eval 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in y around 0 73.7%

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

      1. exp-to-pow 73.7%

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

      2. sub-neg 73.7%

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

      3. metadata-eval 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in b around 0 89.6%

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

      1. unpow-prod-up 89.6%

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

      2. unpow-1 89.6%

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

   9. Applied egg-rr 89.6%

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

       1. associate-*r/ 89.6%

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

       2. *-rgt-identity 89.6%

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

   11. Simplified 89.6%

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

   if -9.0000000000000001e33 < t < 1.44999999999999996e-292

   1. Initial program 96.6%

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

      1. associate-*l/ 86.7%

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

      2. *-commutative 86.7%

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

      3. exp-diff 77.3%

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

      4. exp-sum 75.8%

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

      5. *-commutative 75.8%

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

      6. exp-to-pow 75.8%

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

      7. *-commutative 75.8%

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

      8. exp-to-pow 76.8%

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

      9. sub-neg 76.8%

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

      10. metadata-eval 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in t around 0 83.5%

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

      1. times-frac 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in y around 0 85.4%

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

   if 1.44999999999999996e-292 < t < 0.00104999999999999994

   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. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in b around 0 84.3%

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

      1. div-exp 84.4%

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

      2. *-commutative 84.4%

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

      3. exp-to-pow 84.4%

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

      4. rem-exp-log 85.6%

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

   7. Simplified 85.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 0.00105:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 7: 74.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-290}:\\ \;\;\;\;\frac{1}{\left(y \cdot a\right) \cdot \frac{e^{b}}{x}}\\ \mathbf{elif}\;t \leq 0.00115:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -3.7e+34)
     t_1
     (if (<= t 6e-290)
       (/ 1.0 (* (* y a) (/ (exp b) x)))
       (if (<= t 0.00115) (/ (* 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 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -3.7e+34) {
		tmp = t_1;
	} else if (t <= 6e-290) {
		tmp = 1.0 / ((y * a) * (exp(b) / x));
	} else if (t <= 0.00115) {
		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 = (x * ((a ** t) / a)) / y
    if (t <= (-3.7d+34)) then
        tmp = t_1
    else if (t <= 6d-290) then
        tmp = 1.0d0 / ((y * a) * (exp(b) / x))
    else if (t <= 0.00115d0) 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 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -3.7e+34) {
		tmp = t_1;
	} else if (t <= 6e-290) {
		tmp = 1.0 / ((y * a) * (Math.exp(b) / x));
	} else if (t <= 0.00115) {
		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 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -3.7e+34:
		tmp = t_1
	elif t <= 6e-290:
		tmp = 1.0 / ((y * a) * (math.exp(b) / x))
	elif t <= 0.00115:
		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(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -3.7e+34)
		tmp = t_1;
	elseif (t <= 6e-290)
		tmp = Float64(1.0 / Float64(Float64(y * a) * Float64(exp(b) / x)));
	elseif (t <= 0.00115)
		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 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -3.7e+34)
		tmp = t_1;
	elseif (t <= 6e-290)
		tmp = 1.0 / ((y * a) * (exp(b) / x));
	elseif (t <= 0.00115)
		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[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -3.7e+34], t$95$1, If[LessEqual[t, 6e-290], N[(1.0 / N[(N[(y * a), $MachinePrecision] * N[(N[Exp[b], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00115], 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 t < -3.70000000000000009e34 or 0.00115 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 87.6%

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

      2. *-commutative 87.6%

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

      3. exp-diff 67.3%

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

      4. exp-sum 54.9%

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

      5. *-commutative 54.9%

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

      6. exp-to-pow 54.9%

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

      7. *-commutative 54.9%

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

      8. exp-to-pow 54.9%

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

      9. sub-neg 54.9%

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

      10. metadata-eval 54.9%

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

   3. Simplified 54.9%

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

   4. Taylor expanded in y around 0 74.4%

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

      1. exp-to-pow 74.4%

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

      2. sub-neg 74.4%

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

      3. metadata-eval 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in b around 0 90.4%

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

      1. unpow-prod-up 90.4%

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

      2. unpow-1 90.4%

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

   9. Applied egg-rr 90.4%

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

       1. associate-*r/ 90.4%

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

       2. *-rgt-identity 90.4%

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

   11. Simplified 90.4%

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

   if -3.70000000000000009e34 < t < 5.99999999999999985e-290

   1. Initial program 96.6%

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

      1. associate-*l/ 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-diff 76.1%

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

      4. exp-sum 74.6%

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

      5. *-commutative 74.6%

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

      6. exp-to-pow 74.6%

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

      7. *-commutative 74.6%

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

      8. exp-to-pow 75.6%

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

      9. sub-neg 75.6%

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

      10. metadata-eval 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around 0 75.8%

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

      1. exp-to-pow 77.3%

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

      2. sub-neg 77.3%

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

      3. metadata-eval 77.3%

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

   6. Simplified 77.3%

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

      1. clear-num 77.2%

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

      2. inv-pow 77.2%

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

      3. *-commutative 77.2%

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

   8. Applied egg-rr 77.2%

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

      1. unpow-1 77.2%

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

      2. times-frac 84.5%

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

   10. Simplified 84.5%

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

   11. Taylor expanded in t around 0 84.1%

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

       1. *-commutative 84.1%

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

   13. Simplified 84.1%

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

   if 5.99999999999999985e-290 < t < 0.00115

   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. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in b around 0 84.3%

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

      1. div-exp 84.4%

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

      2. *-commutative 84.4%

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

      3. exp-to-pow 84.4%

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

      4. rem-exp-log 85.6%

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

   7. Simplified 85.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+34}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-290}:\\ \;\;\;\;\frac{1}{\left(y \cdot a\right) \cdot \frac{e^{b}}{x}}\\ \mathbf{elif}\;t \leq 0.00115:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 8: 75.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+33} \lor \neg \left(t \leq 1.7 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e+33) (not (<= t 1.7e-16)))
   (/ (* x (/ (pow a t) a)) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+33) || !(t <= 1.7e-16)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.05d+33)) .or. (.not. (t <= 1.7d-16))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+33) || !(t <= 1.7e-16)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e+33) or not (t <= 1.7e-16):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e+33) || !(t <= 1.7e-16))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.05e+33) || ~((t <= 1.7e-16)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e+33], N[Not[LessEqual[t, 1.7e-16]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e33 or 1.7e-16 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. exp-diff 65.8%

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

      4. exp-sum 53.8%

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

      5. *-commutative 53.8%

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

      6. exp-to-pow 53.8%

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

      7. *-commutative 53.8%

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

      8. exp-to-pow 53.8%

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

      9. sub-neg 53.8%

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

      10. metadata-eval 53.8%

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

   3. Simplified 53.8%

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

   4. Taylor expanded in y around 0 72.7%

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

      1. exp-to-pow 72.7%

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

      2. sub-neg 72.7%

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

      3. metadata-eval 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in b around 0 88.2%

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

      1. unpow-prod-up 88.2%

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

      2. unpow-1 88.2%

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

   9. Applied egg-rr 88.2%

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

       1. associate-*r/ 88.2%

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

       2. *-rgt-identity 88.2%

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

   11. Simplified 88.2%

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

   if -1.05e33 < t < 1.7e-16

   1. Initial program 96.9%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

      3. exp-diff 74.4%

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

      4. exp-sum 73.7%

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

      5. *-commutative 73.7%

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

      6. exp-to-pow 73.7%

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

      7. *-commutative 73.7%

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

      8. exp-to-pow 75.0%

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

      9. sub-neg 75.0%

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

      10. metadata-eval 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. times-frac 79.5%

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

   6. Simplified 79.5%

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

   7. Taylor expanded in y around 0 76.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+33} \lor \neg \left(t \leq 1.7 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 9: 58.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a \cdot \left(y \cdot e^{b}\right)} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. associate-*l/ 85.3%

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

   2. *-commutative 85.3%

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

   3. exp-diff 70.5%

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

   4. exp-sum 64.6%

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

   5. *-commutative 64.6%

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

   6. exp-to-pow 64.6%

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

   7. *-commutative 64.6%

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

   8. exp-to-pow 65.3%

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

   9. sub-neg 65.3%

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

   10. metadata-eval 65.3%

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

3. Simplified 65.3%

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

4. Taylor expanded in t around 0 70.5%

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

   1. times-frac 67.3%

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

6. Simplified 67.3%

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

7. Taylor expanded in y around 0 64.3%

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

8. Final simplification 64.3%

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

Alternative 10: 39.0% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.4e+20)
   (/ (- (/ x a) (* x (/ b a))) y)
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+20) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.4d+20)) then
        tmp = ((x / a) - (x * (b / a))) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+20) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.4e+20:
		tmp = ((x / a) - (x * (b / a))) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.4e+20)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.4e+20)
		tmp = ((x / a) - (x * (b / a))) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.4e+20], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4e20

   1. Initial program 100.0%

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

      1. associate-*l/ 81.5%

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

      2. *-commutative 81.5%

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

      3. exp-diff 49.2%

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

      4. exp-sum 46.2%

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

      5. *-commutative 46.2%

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

      6. exp-to-pow 46.2%

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

      7. *-commutative 46.2%

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

      8. exp-to-pow 46.2%

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

      9. sub-neg 46.2%

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

      10. metadata-eval 46.2%

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

   3. Simplified 46.2%

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

   4. Taylor expanded in t around 0 64.8%

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

      1. times-frac 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in y around 0 80.3%

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

   8. Taylor expanded in b around 0 33.2%

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

   9. Taylor expanded in y around 0 40.5%

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

       1. +-commutative 40.5%

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

       2. mul-1-neg 40.5%

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

       3. unsub-neg 40.5%

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

       4. *-commutative 40.5%

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

       5. associate-*r/ 43.6%

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

   11. Simplified 43.6%

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

   if -2.4e20 < b

   1. Initial program 97.8%

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

      1. associate-*l/ 86.6%

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

      2. *-commutative 86.6%

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

      3. exp-diff 77.7%

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

      4. exp-sum 70.9%

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

      5. *-commutative 70.9%

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

      6. exp-to-pow 70.9%

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

      7. *-commutative 70.9%

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

      8. exp-to-pow 71.8%

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

      9. sub-neg 71.8%

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

      10. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. times-frac 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in y around 0 58.8%

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

   8. Taylor expanded in b around 0 44.2%

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

      1. distribute-lft-out 46.8%

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

      2. *-commutative 46.8%

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

   10. Simplified 46.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 11: 38.4% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{elif}\;b \leq 45000000000000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e+127)
   (* x (/ (- b) (* y a)))
   (if (<= b 45000000000000.0) (/ x (* y a)) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+127) {
		tmp = x * (-b / (y * a));
	} else if (b <= 45000000000000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d+127)) then
        tmp = x * (-b / (y * a))
    else if (b <= 45000000000000.0d0) then
        tmp = x / (y * a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+127) {
		tmp = x * (-b / (y * a));
	} else if (b <= 45000000000000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e+127:
		tmp = x * (-b / (y * a))
	elif b <= 45000000000000.0:
		tmp = x / (y * a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e+127)
		tmp = Float64(x * Float64(Float64(-b) / Float64(y * a)));
	elseif (b <= 45000000000000.0)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e+127)
		tmp = x * (-b / (y * a));
	elseif (b <= 45000000000000.0)
		tmp = x / (y * a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e+127], N[(x * N[((-b) / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 45000000000000.0], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2000000000000004e127

   1. Initial program 100.0%

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

      1. associate-*l/ 75.0%

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

      2. *-commutative 75.0%

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

      3. exp-diff 52.5%

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

      4. exp-sum 47.5%

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

      5. *-commutative 47.5%

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

      6. exp-to-pow 47.5%

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

      7. *-commutative 47.5%

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

      8. exp-to-pow 47.5%

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

      9. sub-neg 47.5%

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

      10. metadata-eval 47.5%

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

   3. Simplified 47.5%

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

   4. Taylor expanded in t around 0 67.6%

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

      1. times-frac 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in y around 0 90.2%

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

   8. Taylor expanded in b around 0 32.6%

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

   9. Taylor expanded in b around inf 32.6%

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

       1. associate-*r/ 32.6%

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

       2. *-commutative 32.6%

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

       3. neg-mul-1 32.6%

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

       4. distribute-rgt-neg-out 32.6%

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

       5. associate-*r/ 34.8%

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

   11. Simplified 34.8%

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

   if -5.2000000000000004e127 < b < 4.5e13

   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. Step-by-step derivation

      1. associate-*l/ 90.3%

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

      2. *-commutative 90.3%

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

      3. exp-diff 78.5%

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

      4. exp-sum 74.2%

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

      5. *-commutative 74.2%

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

      6. exp-to-pow 74.2%

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

      7. *-commutative 74.2%

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

      8. exp-to-pow 75.3%

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

      9. sub-neg 75.3%

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

      10. metadata-eval 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in t around 0 70.4%

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

      1. times-frac 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in y around 0 52.4%

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

   8. Taylor expanded in b around 0 46.5%

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

      1. *-commutative 46.5%

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

   10. Simplified 46.5%

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

   if 4.5e13 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 78.2%

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

      2. *-commutative 78.2%

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

      3. exp-diff 60.0%

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

      4. exp-sum 49.1%

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

      5. *-commutative 49.1%

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

      6. exp-to-pow 49.1%

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

      7. *-commutative 49.1%

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

      8. exp-to-pow 49.1%

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

      9. sub-neg 49.1%

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

      10. metadata-eval 49.1%

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

   3. Simplified 49.1%

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

   4. Taylor expanded in y around 0 63.8%

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

      1. exp-to-pow 63.8%

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

      2. sub-neg 63.8%

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

      3. metadata-eval 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in t around 0 71.2%

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

   8. Taylor expanded in b around 0 38.2%

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

   9. Taylor expanded in b around inf 39.9%

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

       1. *-commutative 39.9%

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

   11. Simplified 39.9%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \frac{-b}{y \cdot a}\\ \mathbf{elif}\;b \leq 45000000000000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 12: 38.3% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 45000000000000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+97)
   (* (/ x y) (/ (- b) a))
   (if (<= b 45000000000000.0) (/ x (* y a)) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+97) {
		tmp = (x / y) * (-b / a);
	} else if (b <= 45000000000000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.5d+97)) then
        tmp = (x / y) * (-b / a)
    else if (b <= 45000000000000.0d0) then
        tmp = x / (y * a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+97) {
		tmp = (x / y) * (-b / a);
	} else if (b <= 45000000000000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+97:
		tmp = (x / y) * (-b / a)
	elif b <= 45000000000000.0:
		tmp = x / (y * a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+97)
		tmp = Float64(Float64(x / y) * Float64(Float64(-b) / a));
	elseif (b <= 45000000000000.0)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+97)
		tmp = (x / y) * (-b / a);
	elseif (b <= 45000000000000.0)
		tmp = x / (y * a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+97], N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 45000000000000.0], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.49999999999999999e97

   1. Initial program 100.0%

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

      1. associate-*l/ 80.0%

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

      2. *-commutative 80.0%

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

      3. exp-diff 56.0%

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

      4. exp-sum 52.0%

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

      5. *-commutative 52.0%

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

      6. exp-to-pow 52.0%

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

      7. *-commutative 52.0%

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

      8. exp-to-pow 52.0%

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

      9. sub-neg 52.0%

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

      10. metadata-eval 52.0%

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

   3. Simplified 52.0%

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

   4. Taylor expanded in t around 0 70.1%

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

      1. times-frac 62.1%

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

   6. Simplified 62.1%

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

   7. Taylor expanded in y around 0 88.2%

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

   8. Taylor expanded in b around 0 32.7%

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

   9. Taylor expanded in b around inf 32.7%

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

       1. mul-1-neg 32.7%

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

       2. times-frac 36.2%

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

       3. distribute-lft-neg-out 36.2%

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

       4. *-commutative 36.2%

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

       5. distribute-neg-frac 36.2%

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

   11. Simplified 36.2%

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

   if -2.49999999999999999e97 < b < 4.5e13

   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. Step-by-step derivation

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

      3. exp-diff 79.1%

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

      4. exp-sum 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. *-commutative 74.5%

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

      8. exp-to-pow 75.6%

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

      9. sub-neg 75.6%

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

      10. metadata-eval 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in t around 0 69.7%

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

      1. times-frac 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around 0 50.5%

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

   8. Taylor expanded in b around 0 47.9%

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

      1. *-commutative 47.9%

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

   10. Simplified 47.9%

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

   if 4.5e13 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 78.2%

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

      2. *-commutative 78.2%

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

      3. exp-diff 60.0%

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

      4. exp-sum 49.1%

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

      5. *-commutative 49.1%

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

      6. exp-to-pow 49.1%

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

      7. *-commutative 49.1%

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

      8. exp-to-pow 49.1%

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

      9. sub-neg 49.1%

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

      10. metadata-eval 49.1%

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

   3. Simplified 49.1%

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

   4. Taylor expanded in y around 0 63.8%

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

      1. exp-to-pow 63.8%

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

      2. sub-neg 63.8%

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

      3. metadata-eval 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in t around 0 71.2%

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

   8. Taylor expanded in b around 0 38.2%

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

   9. Taylor expanded in b around inf 39.9%

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

       1. *-commutative 39.9%

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

   11. Simplified 39.9%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 45000000000000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 13: 38.3% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+20) (* (/ x y) (/ (- b) a)) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+20) {
		tmp = (x / y) * (-b / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+20)) then
        tmp = (x / y) * (-b / a)
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+20) {
		tmp = (x / y) * (-b / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+20:
		tmp = (x / y) * (-b / a)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+20)
		tmp = Float64(Float64(x / y) * Float64(Float64(-b) / a));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+20)
		tmp = (x / y) * (-b / a);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+20], N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2e20

   1. Initial program 100.0%

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

      1. associate-*l/ 81.5%

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

      2. *-commutative 81.5%

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

      3. exp-diff 49.2%

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

      4. exp-sum 46.2%

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

      5. *-commutative 46.2%

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

      6. exp-to-pow 46.2%

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

      7. *-commutative 46.2%

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

      8. exp-to-pow 46.2%

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

      9. sub-neg 46.2%

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

      10. metadata-eval 46.2%

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

   3. Simplified 46.2%

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

   4. Taylor expanded in t around 0 64.8%

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

      1. times-frac 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in y around 0 80.3%

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

   8. Taylor expanded in b around 0 33.2%

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

   9. Taylor expanded in b around inf 33.2%

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

       1. mul-1-neg 33.2%

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

       2. times-frac 34.5%

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

       3. distribute-lft-neg-out 34.5%

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

       4. *-commutative 34.5%

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

       5. distribute-neg-frac 34.5%

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

   11. Simplified 34.5%

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

   if -2e20 < b

   1. Initial program 97.8%

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

      1. associate-*l/ 86.6%

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

      2. *-commutative 86.6%

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

      3. exp-diff 77.7%

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

      4. exp-sum 70.9%

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

      5. *-commutative 70.9%

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

      6. exp-to-pow 70.9%

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

      7. *-commutative 70.9%

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

      8. exp-to-pow 71.8%

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

      9. sub-neg 71.8%

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

      10. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. times-frac 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in y around 0 58.8%

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

   8. Taylor expanded in b around 0 44.2%

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

      1. distribute-lft-out 46.8%

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

      2. *-commutative 46.8%

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

   10. Simplified 46.8%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 31.7% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.7e-222) (/ x (* y a)) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.7e-222) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.7d-222) then
        tmp = x / (y * a)
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.7e-222) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.7e-222:
		tmp = x / (y * a)
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.7e-222)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.7e-222)
		tmp = x / (y * a);
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.7e-222], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.7000000000000001e-222

   1. Initial program 98.4%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. exp-diff 74.1%

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

      4. exp-sum 68.7%

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

      5. *-commutative 68.7%

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

      6. exp-to-pow 68.7%

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

      7. *-commutative 68.7%

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

      8. exp-to-pow 69.3%

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

      9. sub-neg 69.3%

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

      10. metadata-eval 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. times-frac 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in y around 0 70.9%

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

   8. Taylor expanded in b around 0 44.2%

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

      1. *-commutative 44.2%

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

   10. Simplified 44.2%

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

   if 1.7000000000000001e-222 < t

   1. Initial program 98.3%

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

      1. associate-*l/ 85.1%

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

      2. *-commutative 85.1%

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

      3. exp-diff 65.4%

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

      4. exp-sum 58.9%

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

      5. *-commutative 58.9%

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

      6. exp-to-pow 58.9%

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

      7. *-commutative 58.9%

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

      8. exp-to-pow 59.8%

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

      9. sub-neg 59.8%

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

      10. metadata-eval 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in t around 0 60.5%

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

      1. times-frac 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in y around 0 55.1%

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

   8. Taylor expanded in b around 0 25.8%

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

      1. *-commutative 25.8%

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

   10. Simplified 25.8%

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

       1. associate-/r* 29.9%

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

       2. div-inv 29.8%

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

   12. Applied egg-rr 29.8%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]

Alternative 15: 31.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.8 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.8e-222) (/ x (* y a)) (/ 1.0 (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.8e-222) {
		tmp = x / (y * a);
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.8d-222) then
        tmp = x / (y * a)
    else
        tmp = 1.0d0 / (a * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.8e-222) {
		tmp = x / (y * a);
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.8e-222:
		tmp = x / (y * a)
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.8e-222)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.8e-222)
		tmp = x / (y * a);
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.8e-222], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.79999999999999987e-222

   1. Initial program 98.4%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. exp-diff 74.1%

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

      4. exp-sum 68.7%

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

      5. *-commutative 68.7%

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

      6. exp-to-pow 68.7%

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

      7. *-commutative 68.7%

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

      8. exp-to-pow 69.3%

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

      9. sub-neg 69.3%

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

      10. metadata-eval 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. times-frac 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in y around 0 70.9%

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

   8. Taylor expanded in b around 0 44.2%

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

      1. *-commutative 44.2%

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

   10. Simplified 44.2%

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

   if 1.79999999999999987e-222 < t

   1. Initial program 98.3%

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

      1. associate-*l/ 85.1%

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

      2. *-commutative 85.1%

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

      3. exp-diff 65.4%

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

      4. exp-sum 58.9%

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

      5. *-commutative 58.9%

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

      6. exp-to-pow 58.9%

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

      7. *-commutative 58.9%

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

      8. exp-to-pow 59.8%

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

      9. sub-neg 59.8%

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

      10. metadata-eval 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in t around 0 60.5%

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

      1. times-frac 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in y around 0 55.1%

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

   8. Taylor expanded in b around 0 25.8%

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

      1. *-commutative 25.8%

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

   10. Simplified 25.8%

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

       1. *-commutative 25.8%

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

       2. associate-/r* 28.2%

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

       3. clear-num 28.7%

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

       4. inv-pow 28.7%

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

   12. Applied egg-rr 28.7%

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

       1. unpow-1 28.7%

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

       2. associate-/r/ 31.4%

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

   14. Simplified 31.4%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.8 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 16: 34.9% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 45000000000000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 45000000000000.0) (/ x (* y a)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 45000000000000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 45000000000000.0d0) then
        tmp = x / (y * a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 45000000000000.0) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 45000000000000.0:
		tmp = x / (y * a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 45000000000000.0)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 45000000000000.0)
		tmp = x / (y * a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 45000000000000.0], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.5e13

   1. Initial program 97.9%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

      3. exp-diff 73.3%

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

      4. exp-sum 68.9%

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

      5. *-commutative 68.9%

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

      6. exp-to-pow 68.9%

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

      7. *-commutative 68.9%

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

      8. exp-to-pow 69.8%

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

      9. sub-neg 69.8%

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

      10. metadata-eval 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in t around 0 69.8%

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

      1. times-frac 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in y around 0 59.9%

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

   8. Taylor expanded in b around 0 41.2%

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

      1. *-commutative 41.2%

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

   10. Simplified 41.2%

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

   if 4.5e13 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 78.2%

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

      2. *-commutative 78.2%

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

      3. exp-diff 60.0%

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

      4. exp-sum 49.1%

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

      5. *-commutative 49.1%

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

      6. exp-to-pow 49.1%

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

      7. *-commutative 49.1%

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

      8. exp-to-pow 49.1%

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

      9. sub-neg 49.1%

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

      10. metadata-eval 49.1%

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

   3. Simplified 49.1%

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

   4. Taylor expanded in y around 0 63.8%

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

      1. exp-to-pow 63.8%

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

      2. sub-neg 63.8%

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

      3. metadata-eval 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in t around 0 71.2%

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

   8. Taylor expanded in b around 0 38.2%

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

   9. Taylor expanded in b around inf 39.9%

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

       1. *-commutative 39.9%

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

   11. Simplified 39.9%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 45000000000000:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 17: 30.4% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. associate-*l/ 85.3%

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

   2. *-commutative 85.3%

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

   3. exp-diff 70.5%

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

   4. exp-sum 64.6%

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

   5. *-commutative 64.6%

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

   6. exp-to-pow 64.6%

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

   7. *-commutative 64.6%

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

   8. exp-to-pow 65.3%

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

   9. sub-neg 65.3%

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

   10. metadata-eval 65.3%

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

3. Simplified 65.3%

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

4. Taylor expanded in t around 0 70.5%

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

   1. times-frac 67.3%

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

6. Simplified 67.3%

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

7. Taylor expanded in y around 0 64.3%

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

8. Taylor expanded in b around 0 36.5%

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

   1. *-commutative 36.5%

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

10. Simplified 36.5%

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

11. Final simplification 36.5%

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

Developer target: 71.1% 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 2023336 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

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