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

Percentage Accurate: 98.4% → 98.4%

Time: 24.3s

Alternatives: 20

Speedup: 1.0×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

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: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+46} \lor \neg \left(y \leq 0.0002\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+46) (not (<= y 0.0002)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+46) || !(y <= 0.0002)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 <= (-1.1d+46)) .or. (.not. (y <= 0.0002d0))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 <= -1.1e+46) || !(y <= 0.0002)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / 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 <= -1.1e+46) or not (y <= 0.0002):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / 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 <= -1.1e+46) || !(y <= 0.0002))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / 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 <= -1.1e+46) || ~((y <= 0.0002)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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, -1.1e+46], N[Not[LessEqual[y, 0.0002]], $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], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e46 or 2.0000000000000001e-4 < 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 93.6%

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

      1. mul-1-neg 93.6%

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

   4. Simplified 93.6%

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

   if -1.1e46 < y < 2.0000000000000001e-4

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 96.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+46} \lor \neg \left(y \leq 0.0002\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 81.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 3.3:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y))
        (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -2.4e+46)
     t_2
     (if (<= y 2.15e-257)
       t_1
       (if (<= y 1.04e-231)
         (/ (* x (pow a t)) (* y a))
         (if (<= y 3.3) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -2.4e+46) {
		tmp = t_2;
	} else if (y <= 2.15e-257) {
		tmp = t_1;
	} else if (y <= 1.04e-231) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 3.3) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-2.4d+46)) then
        tmp = t_2
    else if (y <= 2.15d-257) then
        tmp = t_1
    else if (y <= 1.04d-231) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 3.3d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -2.4e+46) {
		tmp = t_2;
	} else if (y <= 2.15e-257) {
		tmp = t_1;
	} else if (y <= 1.04e-231) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 3.3) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -2.4e+46:
		tmp = t_2
	elif y <= 2.15e-257:
		tmp = t_1
	elif y <= 1.04e-231:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 3.3:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y)
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -2.4e+46)
		tmp = t_2;
	elseif (y <= 2.15e-257)
		tmp = t_1;
	elseif (y <= 1.04e-231)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 3.3)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -2.4e+46)
		tmp = t_2;
	elseif (y <= 2.15e-257)
		tmp = t_1;
	elseif (y <= 1.04e-231)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 3.3)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.4e+46], t$95$2, If[LessEqual[y, 2.15e-257], t$95$1, If[LessEqual[y, 1.04e-231], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000008e46 or 3.2999999999999998 < 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 93.5%

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

      1. mul-1-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -2.40000000000000008e46 < y < 2.14999999999999999e-257 or 1.03999999999999998e-231 < y < 3.2999999999999998

   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 97.3%

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

      1. exp-diff 84.7%

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

      2. sub-neg 84.7%

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

      3. metadata-eval 84.7%

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

      4. *-commutative 84.7%

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

      5. exp-to-pow 85.8%

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

   4. Simplified 85.8%

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

   if 2.14999999999999999e-257 < y < 1.03999999999999998e-231

   1. Initial program 85.1%

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

      1. associate-*r/ 97.6%

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

      2. sub-neg 97.6%

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

      3. exp-sum 54.7%

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

      4. associate-/l* 54.7%

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

      5. associate-/r/ 54.7%

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

      6. exp-neg 54.7%

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

      7. associate-*r/ 54.7%

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

   3. Simplified 56.9%

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

   4. Taylor expanded in y around 0 57.1%

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

   5. Taylor expanded in b around 0 100.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-257}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 3.3:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 4: 79.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t + -1 \leq 5 \cdot 10^{+142} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+66)
   (/ (* x (pow a t)) (* y a))
   (if (<= (+ t -1.0) 2e+16)
     (* x (/ (pow z y) (* y (* a (exp b)))))
     (if (or (<= (+ t -1.0) 5e+142) (not (<= (+ t -1.0) 2e+157)))
       (/ (* x (pow a (+ t -1.0))) y)
       (/ (/ (/ x a) (exp b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+66) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 2e+16) {
		tmp = x * (pow(z, y) / (y * (a * exp(b))));
	} else if (((t + -1.0) <= 5e+142) || !((t + -1.0) <= 2e+157)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = ((x / a) / exp(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)) <= (-5d+66)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t + (-1.0d0)) <= 2d+16) then
        tmp = x * ((z ** y) / (y * (a * exp(b))))
    else if (((t + (-1.0d0)) <= 5d+142) .or. (.not. ((t + (-1.0d0)) <= 2d+157))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = ((x / a) / exp(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) <= -5e+66) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 2e+16) {
		tmp = x * (Math.pow(z, y) / (y * (a * Math.exp(b))));
	} else if (((t + -1.0) <= 5e+142) || !((t + -1.0) <= 2e+157)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = ((x / a) / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+66:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t + -1.0) <= 2e+16:
		tmp = x * (math.pow(z, y) / (y * (a * math.exp(b))))
	elif ((t + -1.0) <= 5e+142) or not ((t + -1.0) <= 2e+157):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = ((x / a) / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+66)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t + -1.0) <= 2e+16)
		tmp = Float64(x * Float64((z ^ y) / Float64(y * Float64(a * exp(b)))));
	elseif ((Float64(t + -1.0) <= 5e+142) || !(Float64(t + -1.0) <= 2e+157))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(Float64(x / a) / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+66)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t + -1.0) <= 2e+16)
		tmp = x * ((z ^ y) / (y * (a * exp(b))));
	elseif (((t + -1.0) <= 5e+142) || ~(((t + -1.0) <= 2e+157)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = ((x / a) / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+66], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+16], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], 5e+142], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+157]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 t 1) < -4.99999999999999991e66

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 68.2%

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

      4. associate-/l* 68.2%

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

      5. associate-/r/ 68.2%

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

      6. exp-neg 68.2%

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

      7. associate-*r/ 68.2%

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

   3. Simplified 52.3%

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

   4. Taylor expanded in y around 0 61.5%

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

   5. Taylor expanded in b around 0 82.1%

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

   if -4.99999999999999991e66 < (-.f64 t 1) < 2e16

   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-*r/ 95.6%

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

      2. sub-neg 95.6%

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

      3. exp-sum 88.5%

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

      4. associate-/l* 88.5%

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

      5. associate-/r/ 84.2%

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

      6. exp-neg 84.2%

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

      7. associate-*r/ 84.2%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in t around 0 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*l* 86.8%

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

      3. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if 2e16 < (-.f64 t 1) < 5.0000000000000001e142 or 1.99999999999999997e157 < (-.f64 t 1)

   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 y around 0 95.5%

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

      1. exp-diff 67.7%

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

      2. sub-neg 67.7%

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

      3. metadata-eval 67.7%

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

      4. *-commutative 67.7%

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

      5. exp-to-pow 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in b around 0 86.4%

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

   if 5.0000000000000001e142 < (-.f64 t 1) < 1.99999999999999997e157

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-lft-identity 87.0%

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

      4. +-commutative 87.0%

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

      5. exp-sum 87.0%

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

      6. rem-exp-log 87.0%

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

      7. associate-/r* 87.0%

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

   7. Simplified 87.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t + -1 \leq 5 \cdot 10^{+142} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \end{array} \]

Alternative 5: 77.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+16}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{\frac{x}{y}}{e^{b}}\\ \mathbf{elif}\;t + -1 \leq 5 \cdot 10^{+142} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+66)
   (/ (* x (pow a t)) (* y a))
   (if (<= (+ t -1.0) 2e+16)
     (* (/ (pow z y) a) (/ (/ x y) (exp b)))
     (if (or (<= (+ t -1.0) 5e+142) (not (<= (+ t -1.0) 2e+157)))
       (/ (* x (pow a (+ t -1.0))) y)
       (/ (/ (/ x a) (exp b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+66) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 2e+16) {
		tmp = (pow(z, y) / a) * ((x / y) / exp(b));
	} else if (((t + -1.0) <= 5e+142) || !((t + -1.0) <= 2e+157)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = ((x / a) / exp(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)) <= (-5d+66)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t + (-1.0d0)) <= 2d+16) then
        tmp = ((z ** y) / a) * ((x / y) / exp(b))
    else if (((t + (-1.0d0)) <= 5d+142) .or. (.not. ((t + (-1.0d0)) <= 2d+157))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = ((x / a) / exp(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) <= -5e+66) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 2e+16) {
		tmp = (Math.pow(z, y) / a) * ((x / y) / Math.exp(b));
	} else if (((t + -1.0) <= 5e+142) || !((t + -1.0) <= 2e+157)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = ((x / a) / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+66:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t + -1.0) <= 2e+16:
		tmp = (math.pow(z, y) / a) * ((x / y) / math.exp(b))
	elif ((t + -1.0) <= 5e+142) or not ((t + -1.0) <= 2e+157):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = ((x / a) / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+66)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t + -1.0) <= 2e+16)
		tmp = Float64(Float64((z ^ y) / a) * Float64(Float64(x / y) / exp(b)));
	elseif ((Float64(t + -1.0) <= 5e+142) || !(Float64(t + -1.0) <= 2e+157))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(Float64(x / a) / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+66)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t + -1.0) <= 2e+16)
		tmp = ((z ^ y) / a) * ((x / y) / exp(b));
	elseif (((t + -1.0) <= 5e+142) || ~(((t + -1.0) <= 2e+157)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = ((x / a) / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+66], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+16], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], 5e+142], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+157]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 t 1) < -4.99999999999999991e66

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 68.2%

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

      4. associate-/l* 68.2%

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

      5. associate-/r/ 68.2%

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

      6. exp-neg 68.2%

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

      7. associate-*r/ 68.2%

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

   3. Simplified 52.3%

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

   4. Taylor expanded in y around 0 61.5%

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

   5. Taylor expanded in b around 0 82.1%

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

   if -4.99999999999999991e66 < (-.f64 t 1) < 2e16

   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-*r/ 95.6%

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

      2. sub-neg 95.6%

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

      3. exp-sum 88.5%

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

      4. associate-/l* 88.5%

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

      5. associate-/r/ 84.2%

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

      6. exp-neg 84.2%

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

      7. associate-*r/ 84.2%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in t around 0 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l* 87.7%

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

      3. *-commutative 87.7%

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

      4. times-frac 89.4%

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

      5. associate-/r* 87.3%

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

   6. Simplified 87.3%

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

   if 2e16 < (-.f64 t 1) < 5.0000000000000001e142 or 1.99999999999999997e157 < (-.f64 t 1)

   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 y around 0 95.5%

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

      1. exp-diff 67.7%

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

      2. sub-neg 67.7%

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

      3. metadata-eval 67.7%

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

      4. *-commutative 67.7%

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

      5. exp-to-pow 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in b around 0 86.4%

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

   if 5.0000000000000001e142 < (-.f64 t 1) < 1.99999999999999997e157

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-lft-identity 87.0%

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

      4. +-commutative 87.0%

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

      5. exp-sum 87.0%

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

      6. rem-exp-log 87.0%

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

      7. associate-/r* 87.0%

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

   7. Simplified 87.0%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+16}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{\frac{x}{y}}{e^{b}}\\ \mathbf{elif}\;t + -1 \leq 5 \cdot 10^{+142} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \end{array} \]

Alternative 6: 88.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+47} \lor \neg \left(y \leq 5.1\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.2e+47) (not (<= y 5.1)))
   (/ (* 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+47) || !(y <= 5.1)) {
		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+47)) .or. (.not. (y <= 5.1d0))) 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+47) || !(y <= 5.1)) {
		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+47) or not (y <= 5.1):
		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+47) || !(y <= 5.1))
		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+47) || ~((y <= 5.1)))
		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+47], N[Not[LessEqual[y, 5.1]], $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 < -7.20000000000000015e47 or 5.0999999999999996 < 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 93.5%

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

      1. mul-1-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -7.20000000000000015e47 < y < 5.0999999999999996

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 96.7%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+47} \lor \neg \left(y \leq 5.1\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 7: 79.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+46} \lor \neg \left(y \leq 8.2\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e+46) (not (<= y 8.2)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (/ (pow a (+ t -1.0)) (exp b)) (/ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e+46) || !(y <= 8.2)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (pow(a, (t + -1.0)) / exp(b)) / (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 ((y <= (-8.2d+46)) .or. (.not. (y <= 8.2d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = ((a ** (t + (-1.0d0))) / exp(b)) / (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 ((y <= -8.2e+46) || !(y <= 8.2)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (Math.pow(a, (t + -1.0)) / Math.exp(b)) / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e+46) or not (y <= 8.2):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (math.pow(a, (t + -1.0)) / math.exp(b)) / (y / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e+46) || !(y <= 8.2))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e+46) || ~((y <= 8.2)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = ((a ^ (t + -1.0)) / exp(b)) / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e+46], N[Not[LessEqual[y, 8.2]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999999e46 or 8.1999999999999993 < 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 93.5%

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

      1. mul-1-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -8.19999999999999999e46 < y < 8.1999999999999993

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 96.7%

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

      1. associate-/l* 94.9%

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

      2. exp-diff 83.0%

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

      3. sub-neg 83.0%

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

      4. metadata-eval 83.0%

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

      5. *-commutative 83.0%

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

      6. exp-to-pow 84.1%

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

   4. Simplified 84.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+46} \lor \neg \left(y \leq 8.2\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 73.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{t}}{y \cdot a}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ t_3 := \frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a t)) (* y a)))
        (t_2 (/ (* x (/ (pow z y) a)) y))
        (t_3 (/ (/ x y) (* a (exp b)))))
   (if (<= y -9e+47)
     t_2
     (if (<= y -6.5e-73)
       t_1
       (if (<= y 1.75e-272)
         t_3
         (if (<= y 1.42e-231) t_1 (if (<= y 7.2) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, t)) / (y * a);
	double t_2 = (x * (pow(z, y) / a)) / y;
	double t_3 = (x / y) / (a * exp(b));
	double tmp;
	if (y <= -9e+47) {
		tmp = t_2;
	} else if (y <= -6.5e-73) {
		tmp = t_1;
	} else if (y <= 1.75e-272) {
		tmp = t_3;
	} else if (y <= 1.42e-231) {
		tmp = t_1;
	} else if (y <= 7.2) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (x * (a ** t)) / (y * a)
    t_2 = (x * ((z ** y) / a)) / y
    t_3 = (x / y) / (a * exp(b))
    if (y <= (-9d+47)) then
        tmp = t_2
    else if (y <= (-6.5d-73)) then
        tmp = t_1
    else if (y <= 1.75d-272) then
        tmp = t_3
    else if (y <= 1.42d-231) then
        tmp = t_1
    else if (y <= 7.2d0) then
        tmp = t_3
    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 = (x * Math.pow(a, t)) / (y * a);
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double t_3 = (x / y) / (a * Math.exp(b));
	double tmp;
	if (y <= -9e+47) {
		tmp = t_2;
	} else if (y <= -6.5e-73) {
		tmp = t_1;
	} else if (y <= 1.75e-272) {
		tmp = t_3;
	} else if (y <= 1.42e-231) {
		tmp = t_1;
	} else if (y <= 7.2) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, t)) / (y * a)
	t_2 = (x * (math.pow(z, y) / a)) / y
	t_3 = (x / y) / (a * math.exp(b))
	tmp = 0
	if y <= -9e+47:
		tmp = t_2
	elif y <= -6.5e-73:
		tmp = t_1
	elif y <= 1.75e-272:
		tmp = t_3
	elif y <= 1.42e-231:
		tmp = t_1
	elif y <= 7.2:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ t)) / Float64(y * a))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	t_3 = Float64(Float64(x / y) / Float64(a * exp(b)))
	tmp = 0.0
	if (y <= -9e+47)
		tmp = t_2;
	elseif (y <= -6.5e-73)
		tmp = t_1;
	elseif (y <= 1.75e-272)
		tmp = t_3;
	elseif (y <= 1.42e-231)
		tmp = t_1;
	elseif (y <= 7.2)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ t)) / (y * a);
	t_2 = (x * ((z ^ y) / a)) / y;
	t_3 = (x / y) / (a * exp(b));
	tmp = 0.0;
	if (y <= -9e+47)
		tmp = t_2;
	elseif (y <= -6.5e-73)
		tmp = t_1;
	elseif (y <= 1.75e-272)
		tmp = t_3;
	elseif (y <= 1.42e-231)
		tmp = t_1;
	elseif (y <= 7.2)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+47], t$95$2, If[LessEqual[y, -6.5e-73], t$95$1, If[LessEqual[y, 1.75e-272], t$95$3, If[LessEqual[y, 1.42e-231], t$95$1, If[LessEqual[y, 7.2], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999958e47 or 7.20000000000000018 < 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 93.5%

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

      1. mul-1-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -8.99999999999999958e47 < y < -6.4999999999999999e-73 or 1.7499999999999998e-272 < y < 1.42000000000000014e-231

   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. Step-by-step derivation

      1. associate-*r/ 99.3%

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

      2. sub-neg 99.3%

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

      3. exp-sum 78.2%

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

      4. associate-/l* 78.2%

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

      5. associate-/r/ 78.2%

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

      6. exp-neg 78.2%

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

      7. associate-*r/ 78.2%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in y around 0 76.3%

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

   5. Taylor expanded in b around 0 81.9%

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

   if -6.4999999999999999e-73 < y < 1.7499999999999998e-272 or 1.42000000000000014e-231 < y < 7.20000000000000018

   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-*r/ 93.9%

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

      2. sub-neg 93.9%

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

      3. exp-sum 82.4%

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

      4. associate-/l* 82.4%

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

      5. associate-/r/ 76.2%

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

      6. exp-neg 76.2%

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

      7. associate-*r/ 76.2%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in t around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. associate-*l* 80.5%

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

      3. *-commutative 80.5%

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

   6. Simplified 80.5%

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

   7. Taylor expanded in y around 0 81.9%

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

   8. Taylor expanded in a around 0 81.9%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 81.9%

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

      4. associate-/r* 84.4%

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

   10. Simplified 84.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-272}:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 7.2:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 9: 73.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-231}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.76:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)) (t_2 (/ (/ x y) (* a (exp b)))))
   (if (<= y -7e+45)
     t_1
     (if (<= y -6e-77)
       (/ (* x (pow a t)) (* y a))
       (if (<= y 1.35e-270)
         t_2
         (if (<= y 5.2e-231)
           (/ (pow a (+ t -1.0)) (/ y x))
           (if (<= y 1.76) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double t_2 = (x / y) / (a * exp(b));
	double tmp;
	if (y <= -7e+45) {
		tmp = t_1;
	} else if (y <= -6e-77) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 1.35e-270) {
		tmp = t_2;
	} else if (y <= 5.2e-231) {
		tmp = pow(a, (t + -1.0)) / (y / x);
	} else if (y <= 1.76) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    t_2 = (x / y) / (a * exp(b))
    if (y <= (-7d+45)) then
        tmp = t_1
    else if (y <= (-6d-77)) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 1.35d-270) then
        tmp = t_2
    else if (y <= 5.2d-231) then
        tmp = (a ** (t + (-1.0d0))) / (y / x)
    else if (y <= 1.76d0) then
        tmp = t_2
    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(z, y) / a)) / y;
	double t_2 = (x / y) / (a * Math.exp(b));
	double tmp;
	if (y <= -7e+45) {
		tmp = t_1;
	} else if (y <= -6e-77) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 1.35e-270) {
		tmp = t_2;
	} else if (y <= 5.2e-231) {
		tmp = Math.pow(a, (t + -1.0)) / (y / x);
	} else if (y <= 1.76) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	t_2 = (x / y) / (a * math.exp(b))
	tmp = 0
	if y <= -7e+45:
		tmp = t_1
	elif y <= -6e-77:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 1.35e-270:
		tmp = t_2
	elif y <= 5.2e-231:
		tmp = math.pow(a, (t + -1.0)) / (y / x)
	elif y <= 1.76:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	t_2 = Float64(Float64(x / y) / Float64(a * exp(b)))
	tmp = 0.0
	if (y <= -7e+45)
		tmp = t_1;
	elseif (y <= -6e-77)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 1.35e-270)
		tmp = t_2;
	elseif (y <= 5.2e-231)
		tmp = Float64((a ^ Float64(t + -1.0)) / Float64(y / x));
	elseif (y <= 1.76)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	t_2 = (x / y) / (a * exp(b));
	tmp = 0.0;
	if (y <= -7e+45)
		tmp = t_1;
	elseif (y <= -6e-77)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 1.35e-270)
		tmp = t_2;
	elseif (y <= 5.2e-231)
		tmp = (a ^ (t + -1.0)) / (y / x);
	elseif (y <= 1.76)
		tmp = t_2;
	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[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+45], t$95$1, If[LessEqual[y, -6e-77], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-270], t$95$2, If[LessEqual[y, 5.2e-231], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.76], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.00000000000000046e45 or 1.76000000000000001 < 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 93.5%

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

      1. mul-1-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -7.00000000000000046e45 < y < -6.00000000000000033e-77

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 80.8%

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

      4. associate-/l* 80.8%

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

      5. associate-/r/ 80.8%

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

      6. exp-neg 80.8%

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

      7. associate-*r/ 80.8%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in y around 0 80.8%

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

   5. Taylor expanded in b around 0 81.2%

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

   if -6.00000000000000033e-77 < y < 1.35000000000000004e-270 or 5.20000000000000006e-231 < y < 1.76000000000000001

   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-*r/ 93.9%

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

      2. sub-neg 93.9%

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

      3. exp-sum 82.4%

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

      4. associate-/l* 82.4%

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

      5. associate-/r/ 76.2%

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

      6. exp-neg 76.2%

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

      7. associate-*r/ 76.2%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in t around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. associate-*l* 80.5%

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

      3. *-commutative 80.5%

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

   6. Simplified 80.5%

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

   7. Taylor expanded in y around 0 81.9%

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

   8. Taylor expanded in a around 0 81.9%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 81.9%

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

      4. associate-/r* 84.4%

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

   10. Simplified 84.4%

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

   if 1.35000000000000004e-270 < y < 5.20000000000000006e-231

   1. Initial program 90.5%

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

   2. Taylor expanded in y around 0 90.5%

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

      1. exp-diff 65.5%

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

      2. sub-neg 65.5%

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

      3. metadata-eval 65.5%

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

      4. *-commutative 65.5%

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

      5. exp-to-pow 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in b around 0 83.3%

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

      1. associate-/l* 91.1%

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

      2. sub-neg 91.1%

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

      3. metadata-eval 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+45}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-231}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.76:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 10: 73.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{\frac{1}{a}}{e^{b}}}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-231}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 0.0275:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -1.15e+46)
     t_1
     (if (<= y -2.5e-78)
       (/ (* x (pow a t)) (* y a))
       (if (<= y 1.52e-270)
         (/ (/ (/ 1.0 a) (exp b)) (/ y x))
         (if (<= y 1.1e-231)
           (/ (pow a (+ t -1.0)) (/ y x))
           (if (<= y 0.0275) (/ (/ x y) (* a (exp b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.15e+46) {
		tmp = t_1;
	} else if (y <= -2.5e-78) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 1.52e-270) {
		tmp = ((1.0 / a) / exp(b)) / (y / x);
	} else if (y <= 1.1e-231) {
		tmp = pow(a, (t + -1.0)) / (y / x);
	} else if (y <= 0.0275) {
		tmp = (x / y) / (a * exp(b));
	} 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 * ((z ** y) / a)) / y
    if (y <= (-1.15d+46)) then
        tmp = t_1
    else if (y <= (-2.5d-78)) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 1.52d-270) then
        tmp = ((1.0d0 / a) / exp(b)) / (y / x)
    else if (y <= 1.1d-231) then
        tmp = (a ** (t + (-1.0d0))) / (y / x)
    else if (y <= 0.0275d0) then
        tmp = (x / y) / (a * exp(b))
    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(z, y) / a)) / y;
	double tmp;
	if (y <= -1.15e+46) {
		tmp = t_1;
	} else if (y <= -2.5e-78) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 1.52e-270) {
		tmp = ((1.0 / a) / Math.exp(b)) / (y / x);
	} else if (y <= 1.1e-231) {
		tmp = Math.pow(a, (t + -1.0)) / (y / x);
	} else if (y <= 0.0275) {
		tmp = (x / y) / (a * Math.exp(b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -1.15e+46:
		tmp = t_1
	elif y <= -2.5e-78:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 1.52e-270:
		tmp = ((1.0 / a) / math.exp(b)) / (y / x)
	elif y <= 1.1e-231:
		tmp = math.pow(a, (t + -1.0)) / (y / x)
	elif y <= 0.0275:
		tmp = (x / y) / (a * math.exp(b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -1.15e+46)
		tmp = t_1;
	elseif (y <= -2.5e-78)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 1.52e-270)
		tmp = Float64(Float64(Float64(1.0 / a) / exp(b)) / Float64(y / x));
	elseif (y <= 1.1e-231)
		tmp = Float64((a ^ Float64(t + -1.0)) / Float64(y / x));
	elseif (y <= 0.0275)
		tmp = Float64(Float64(x / y) / Float64(a * exp(b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -1.15e+46)
		tmp = t_1;
	elseif (y <= -2.5e-78)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 1.52e-270)
		tmp = ((1.0 / a) / exp(b)) / (y / x);
	elseif (y <= 1.1e-231)
		tmp = (a ^ (t + -1.0)) / (y / x);
	elseif (y <= 0.0275)
		tmp = (x / y) / (a * exp(b));
	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[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.15e+46], t$95$1, If[LessEqual[y, -2.5e-78], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-270], N[(N[(N[(1.0 / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-231], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0275], N[(N[(x / y), $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.15e46 or 0.0275000000000000001 < 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 93.5%

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

      1. mul-1-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in b around 0 89.5%

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

      1. div-exp 89.5%

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

      2. *-commutative 89.5%

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

      3. exp-to-pow 89.5%

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

      4. rem-exp-log 89.5%

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

   7. Simplified 89.5%

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

   if -1.15e46 < y < -2.4999999999999998e-78

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 80.8%

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

      4. associate-/l* 80.8%

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

      5. associate-/r/ 80.8%

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

      6. exp-neg 80.8%

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

      7. associate-*r/ 80.8%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in y around 0 80.8%

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

   5. Taylor expanded in b around 0 81.2%

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

   if -2.4999999999999998e-78 < y < 1.52000000000000004e-270

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 94.7%

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

      1. associate-/l* 94.2%

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

      2. exp-diff 86.4%

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

      3. sub-neg 86.4%

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

      4. metadata-eval 86.4%

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

      5. *-commutative 86.4%

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

      6. exp-to-pow 87.9%

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

   4. Simplified 87.9%

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

   5. Taylor expanded in t around 0 86.0%

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

   if 1.52000000000000004e-270 < y < 1.10000000000000005e-231

   1. Initial program 90.5%

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

   2. Taylor expanded in y around 0 90.5%

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

      1. exp-diff 65.5%

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

      2. sub-neg 65.5%

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

      3. metadata-eval 65.5%

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

      4. *-commutative 65.5%

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

      5. exp-to-pow 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in b around 0 83.3%

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

      1. associate-/l* 91.1%

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

      2. sub-neg 91.1%

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

      3. metadata-eval 91.1%

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

   7. Simplified 91.1%

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

   if 1.10000000000000005e-231 < y < 0.0275000000000000001

   1. Initial program 98.6%

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

      1. associate-*r/ 94.8%

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

      2. sub-neg 94.8%

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

      3. exp-sum 81.5%

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

      4. associate-/l* 81.5%

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

      5. associate-/r/ 77.0%

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

      6. exp-neg 77.0%

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

      7. associate-*r/ 77.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in t around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*l* 78.3%

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

      3. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around 0 80.3%

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

   8. Taylor expanded in a around 0 80.3%

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

      1. associate-*r* 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 80.3%

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

      4. associate-/r* 82.5%

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

   10. Simplified 82.5%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a \cdot e^{b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+46}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{\frac{1}{a}}{e^{b}}}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-231}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 0.0275:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 11: 73.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1400000 \lor \neg \left(y \leq 6.2\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1400000.0) (not (<= y 6.2)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (/ x y) (* a (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1400000.0) || !(y <= 6.2)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x / y) / (a * 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 ((y <= (-1400000.0d0)) .or. (.not. (y <= 6.2d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x / y) / (a * 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 ((y <= -1400000.0) || !(y <= 6.2)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x / y) / (a * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1400000.0) or not (y <= 6.2):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x / y) / (a * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1400000.0) || !(y <= 6.2))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x / y) / Float64(a * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1400000.0) || ~((y <= 6.2)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x / y) / (a * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1400000.0], N[Not[LessEqual[y, 6.2]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e6 or 6.20000000000000018 < 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 90.8%

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

      1. mul-1-neg 90.8%

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

   4. Simplified 90.8%

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

   5. Taylor expanded in b around 0 87.0%

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

      1. div-exp 87.0%

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

      2. *-commutative 87.0%

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

      3. exp-to-pow 87.0%

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

      4. rem-exp-log 87.0%

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

   7. Simplified 87.0%

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

   if -1.4e6 < y < 6.20000000000000018

   1. Initial program 96.5%

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

      1. associate-*r/ 95.2%

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

      2. sub-neg 95.2%

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

      3. exp-sum 81.8%

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

      4. associate-/l* 81.8%

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

      5. associate-/r/ 77.1%

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

      6. exp-neg 77.1%

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

      7. associate-*r/ 77.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in t around 0 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-*l* 74.9%

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

      3. *-commutative 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in y around 0 75.9%

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

   8. Taylor expanded in a around 0 75.9%

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

      1. associate-*r* 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*r* 75.9%

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

      4. associate-/r* 76.2%

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

   10. Simplified 76.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1400000 \lor \neg \left(y \leq 6.2\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \end{array} \]

Alternative 12: 58.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot e^{b}\\ \mathbf{if}\;a \leq 3 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{x}{y}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (exp b))))
   (if (<= a 3e-86) (/ (/ x y) t_1) (/ x (* y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * exp(b);
	double tmp;
	if (a <= 3e-86) {
		tmp = (x / y) / t_1;
	} else {
		tmp = x / (y * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * exp(b)
    if (a <= 3d-86) then
        tmp = (x / y) / t_1
    else
        tmp = x / (y * 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 = a * Math.exp(b);
	double tmp;
	if (a <= 3e-86) {
		tmp = (x / y) / t_1;
	} else {
		tmp = x / (y * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * math.exp(b)
	tmp = 0
	if a <= 3e-86:
		tmp = (x / y) / t_1
	else:
		tmp = x / (y * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * exp(b))
	tmp = 0.0
	if (a <= 3e-86)
		tmp = Float64(Float64(x / y) / t_1);
	else
		tmp = Float64(x / Float64(y * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * exp(b);
	tmp = 0.0;
	if (a <= 3e-86)
		tmp = (x / y) / t_1;
	else
		tmp = x / (y * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3e-86], N[(N[(x / y), $MachinePrecision] / t$95$1), $MachinePrecision], N[(x / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 3.0000000000000001e-86

   1. Initial program 99.5%

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

      1. associate-*r/ 95.6%

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

      2. sub-neg 95.6%

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

      3. exp-sum 81.0%

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

      4. associate-/l* 81.0%

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

      5. associate-/r/ 76.5%

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

      6. exp-neg 76.5%

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

      7. associate-*r/ 76.5%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in t around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l* 68.0%

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

      3. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in y around 0 45.5%

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

   8. Taylor expanded in a around 0 45.5%

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

      1. associate-*r* 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-*r* 45.5%

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

      4. associate-/r* 50.9%

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

   10. Simplified 50.9%

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

   if 3.0000000000000001e-86 < a

   1. Initial program 97.6%

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

      1. associate-*r/ 98.7%

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

      2. sub-neg 98.7%

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

      3. exp-sum 79.5%

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

      4. associate-/l* 79.5%

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

      5. associate-/r/ 78.3%

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

      6. exp-neg 78.3%

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

      7. associate-*r/ 78.3%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in t around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*l* 73.5%

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

      3. *-commutative 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in y around 0 61.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{x}{y}}{a \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]

Alternative 13: 58.4% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * N[(a * 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-*r/ 97.6%

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

   2. sub-neg 97.6%

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

   3. exp-sum 80.0%

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

   4. associate-/l* 80.0%

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

   5. associate-/r/ 77.7%

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

   6. exp-neg 77.7%

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

   7. associate-*r/ 77.7%

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

3. Simplified 70.4%

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

4. Taylor expanded in t around 0 71.6%

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

   1. *-commutative 71.6%

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

   2. associate-*l* 71.6%

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

   3. *-commutative 71.6%

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

6. Simplified 71.6%

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

7. Taylor expanded in y around 0 56.1%

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

8. Final simplification 56.1%

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

Alternative 14: 41.0% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{+73}:\\ \;\;\;\;t_1 - \left(\frac{x}{a} \cdot \frac{b}{y} + \left(b \cdot b\right) \cdot \left(t_1 \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)))
   (if (<= b -1.32e+73)
     (- t_1 (+ (* (/ x a) (/ b y)) (* (* b b) (* t_1 -0.5))))
     (/ x (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.32e+73) {
		tmp = t_1 - (((x / a) * (b / y)) + ((b * b) * (t_1 * -0.5)));
	} else {
		tmp = x / (y * (a + (a * 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) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (b <= (-1.32d+73)) then
        tmp = t_1 - (((x / a) * (b / y)) + ((b * b) * (t_1 * (-0.5d0))))
    else
        tmp = x / (y * (a + (a * 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 t_1 = (x / a) / y;
	double tmp;
	if (b <= -1.32e+73) {
		tmp = t_1 - (((x / a) * (b / y)) + ((b * b) * (t_1 * -0.5)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if b <= -1.32e+73:
		tmp = t_1 - (((x / a) * (b / y)) + ((b * b) * (t_1 * -0.5)))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -1.32e+73)
		tmp = Float64(t_1 - Float64(Float64(Float64(x / a) * Float64(b / y)) + Float64(Float64(b * b) * Float64(t_1 * -0.5))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (b <= -1.32e+73)
		tmp = t_1 - (((x / a) * (b / y)) + ((b * b) * (t_1 * -0.5)));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.32e+73], N[(t$95$1 - N[(N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] * N[(t$95$1 * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.32e73

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 65.0%

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

      4. associate-/l* 65.0%

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

      5. associate-/r/ 65.0%

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

      6. exp-neg 65.0%

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

      7. associate-*r/ 65.0%

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

   3. Simplified 61.7%

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

   4. Taylor expanded in t around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-*l* 75.1%

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

      3. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in y around 0 77.0%

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

   8. Taylor expanded in b around 0 45.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + \left(-1 \cdot \frac{b \cdot x}{y \cdot a} + -1 \cdot \left(\left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right) \cdot {b}^{2}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-/r* 45.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} + \left(-1 \cdot \frac{b \cdot x}{y \cdot a} + -1 \cdot \left(\left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right) \cdot {b}^{2}\right)\right) \]

      2. distribute-lft-out 45.8%

         \[\leadsto \frac{\frac{x}{a}}{y} + \color{blue}{-1 \cdot \left(\frac{b \cdot x}{y \cdot a} + \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right) \cdot {b}^{2}\right)} \]

      3. times-frac 39.4%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\color{blue}{\frac{b}{y} \cdot \frac{x}{a}} + \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right) \cdot {b}^{2}\right) \]

      4. distribute-rgt-out 59.4%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \color{blue}{\left(\frac{x}{a \cdot y} \cdot \left(-1 + 0.5\right)\right)} \cdot {b}^{2}\right) \]

      5. metadata-eval 59.4%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \left(\frac{x}{a \cdot y} \cdot \color{blue}{-0.5}\right) \cdot {b}^{2}\right) \]

      6. *-commutative 59.4%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \color{blue}{\left(-0.5 \cdot \frac{x}{a \cdot y}\right)} \cdot {b}^{2}\right) \]

      7. *-commutative 59.4%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \color{blue}{{b}^{2} \cdot \left(-0.5 \cdot \frac{x}{a \cdot y}\right)}\right) \]

      8. unpow2 59.4%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \color{blue}{\left(b \cdot b\right)} \cdot \left(-0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      9. associate-/r* 61.1%

         \[\leadsto \frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \left(b \cdot b\right) \cdot \left(-0.5 \cdot \color{blue}{\frac{\frac{x}{a}}{y}}\right)\right) \]

   10. Simplified 61.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} + -1 \cdot \left(\frac{b}{y} \cdot \frac{x}{a} + \left(b \cdot b\right) \cdot \left(-0.5 \cdot \frac{\frac{x}{a}}{y}\right)\right)} \]

   if -1.32e73 < b

   1. Initial program 97.7%

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

      1. associate-*r/ 96.9%

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

      2. sub-neg 96.9%

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

      3. exp-sum 84.6%

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

      4. associate-/l* 84.6%

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

      5. associate-/r/ 81.6%

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

      6. exp-neg 81.6%

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

      7. associate-*r/ 81.6%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in t around 0 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-*l* 70.5%

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

      3. *-commutative 70.5%

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

   6. Simplified 70.5%

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

   7. Taylor expanded in y around 0 49.8%

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

   8. Taylor expanded in b around 0 37.9%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} - \left(\frac{x}{a} \cdot \frac{b}{y} + \left(b \cdot b\right) \cdot \left(\frac{\frac{x}{a}}{y} \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 15: 38.8% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot b}{y}\\ t_2 := \frac{\frac{x}{y} - t_1}{a}\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{a \cdot \frac{x}{y} + a \cdot t_1}{a \cdot a}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x b) y)) (t_2 (/ (- (/ x y) t_1) a)))
   (if (<= b -3.2e-225)
     t_2
     (if (<= b 4.6e-168)
       (/ (+ (* a (/ x y)) (* a t_1)) (* a a))
       (if (<= b 2.25e-11) t_2 (/ x (* y (+ a (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * b) / y;
	double t_2 = ((x / y) - t_1) / a;
	double tmp;
	if (b <= -3.2e-225) {
		tmp = t_2;
	} else if (b <= 4.6e-168) {
		tmp = ((a * (x / y)) + (a * t_1)) / (a * a);
	} else if (b <= 2.25e-11) {
		tmp = t_2;
	} else {
		tmp = x / (y * (a + (a * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * b) / y
    t_2 = ((x / y) - t_1) / a
    if (b <= (-3.2d-225)) then
        tmp = t_2
    else if (b <= 4.6d-168) then
        tmp = ((a * (x / y)) + (a * t_1)) / (a * a)
    else if (b <= 2.25d-11) then
        tmp = t_2
    else
        tmp = x / (y * (a + (a * 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 t_1 = (x * b) / y;
	double t_2 = ((x / y) - t_1) / a;
	double tmp;
	if (b <= -3.2e-225) {
		tmp = t_2;
	} else if (b <= 4.6e-168) {
		tmp = ((a * (x / y)) + (a * t_1)) / (a * a);
	} else if (b <= 2.25e-11) {
		tmp = t_2;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * b) / y
	t_2 = ((x / y) - t_1) / a
	tmp = 0
	if b <= -3.2e-225:
		tmp = t_2
	elif b <= 4.6e-168:
		tmp = ((a * (x / y)) + (a * t_1)) / (a * a)
	elif b <= 2.25e-11:
		tmp = t_2
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * b) / y)
	t_2 = Float64(Float64(Float64(x / y) - t_1) / a)
	tmp = 0.0
	if (b <= -3.2e-225)
		tmp = t_2;
	elseif (b <= 4.6e-168)
		tmp = Float64(Float64(Float64(a * Float64(x / y)) + Float64(a * t_1)) / Float64(a * a));
	elseif (b <= 2.25e-11)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * b) / y;
	t_2 = ((x / y) - t_1) / a;
	tmp = 0.0;
	if (b <= -3.2e-225)
		tmp = t_2;
	elseif (b <= 4.6e-168)
		tmp = ((a * (x / y)) + (a * t_1)) / (a * a);
	elseif (b <= 2.25e-11)
		tmp = t_2;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x / y), $MachinePrecision] - t$95$1), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b, -3.2e-225], t$95$2, If[LessEqual[b, 4.6e-168], N[(N[(N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e-11], t$95$2, N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.19999999999999975e-225 or 4.59999999999999971e-168 < b < 2.25e-11

   1. Initial program 98.6%

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

      1. associate-*r/ 97.6%

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

      2. sub-neg 97.6%

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

      3. exp-sum 80.0%

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

      4. associate-/l* 80.0%

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

      5. associate-/r/ 80.0%

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

      6. exp-neg 80.0%

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

      7. associate-*r/ 80.0%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*l* 71.2%

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

      3. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in y around 0 49.7%

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

   8. Taylor expanded in b around 0 33.8%

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

      1. mul-1-neg 33.8%

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

      2. unsub-neg 33.8%

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

      3. associate-/r* 32.3%

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

      4. associate-/l* 28.2%

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

      5. associate-/l* 28.2%

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

   10. Simplified 28.2%

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

       1. associate-/l/ 28.6%

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

       2. associate-/r* 30.7%

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

       3. associate-/r/ 32.9%

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

       4. times-frac 34.8%

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

       5. associate-/r* 38.1%

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

       6. sub-div 40.0%

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

       7. *-commutative 40.0%

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

   12. Applied egg-rr 40.0%

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

   if -3.19999999999999975e-225 < b < 4.59999999999999971e-168

   1. Initial program 94.8%

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

      1. associate-*r/ 94.7%

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

      2. sub-neg 94.7%

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

      3. exp-sum 94.7%

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

      4. associate-/l* 94.7%

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

      5. associate-/r/ 94.7%

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

      6. exp-neg 94.7%

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

      7. associate-*r/ 94.7%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around 0 76.8%

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

      1. *-commutative 76.8%

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

      2. associate-*l* 76.8%

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

      3. *-commutative 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around 0 45.4%

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

   8. Taylor expanded in b around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. unsub-neg 38.3%

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

      3. associate-/r* 38.7%

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

      4. associate-/l* 36.3%

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

      5. associate-/l* 34.0%

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

   10. Simplified 34.0%

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

       1. sub-neg 34.0%

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

       2. associate-/l/ 36.7%

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

       3. associate-/r* 38.0%

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

       4. associate-/r/ 38.0%

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

       5. times-frac 34.0%

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

       6. mul-1-neg 34.0%

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

       7. add-sqr-sqrt 28.6%

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

       8. sqrt-unprod 34.0%

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

       9. mul-1-neg 34.0%

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

       10. times-frac 33.3%

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

       11. associate-/r/ 38.0%

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

       12. mul-1-neg 38.0%

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

       13. times-frac 35.6%

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

       14. associate-/r/ 40.3%

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

       15. sqr-neg 40.3%

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

       16. sqrt-unprod 33.1%

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

       17. add-sqr-sqrt 42.6%

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

       18. associate-/r/ 40.3%

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

       19. times-frac 36.3%

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

       20. associate-/r* 41.0%

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

   12. Applied egg-rr 54.3%

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

   if 2.25e-11 < 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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 68.5%

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

      4. associate-/l* 68.5%

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

      5. associate-/r/ 57.4%

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

      6. exp-neg 57.4%

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

      7. associate-*r/ 57.4%

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

   3. Simplified 46.3%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l* 68.6%

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

      3. *-commutative 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in y around 0 83.6%

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

   8. Taylor expanded in b around 0 48.0%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{-225}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{a \cdot \frac{x}{y} + a \cdot \frac{x \cdot b}{y}}{a \cdot a}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 39.7% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.9 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.9e-214)
   (/ (- (/ x y) (/ (* x b) y)) a)
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.9e-214) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (y * (a + (a * 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 <= 4.9d-214) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else
        tmp = x / (y * (a + (a * 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 <= 4.9e-214) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.9e-214:
		tmp = ((x / y) - ((x * b) / y)) / a
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.9e-214)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.9e-214)
		tmp = ((x / y) - ((x * b) / y)) / a;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.9e-214], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.89999999999999968e-214

   1. Initial program 98.7%

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

      1. associate-*r/ 97.6%

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

      2. sub-neg 97.6%

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

      3. exp-sum 79.1%

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

      4. associate-/l* 79.1%

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

      5. associate-/r/ 79.1%

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

      6. exp-neg 79.1%

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

      7. associate-*r/ 79.1%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*l* 73.5%

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

      3. *-commutative 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in y around 0 52.3%

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

   8. Taylor expanded in b around 0 37.7%

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

      1. mul-1-neg 37.7%

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

      2. unsub-neg 37.7%

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

      3. associate-/r* 37.9%

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

      4. associate-/l* 33.6%

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

      5. associate-/l* 33.6%

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

   10. Simplified 33.6%

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

       1. associate-/l/ 33.9%

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

       2. associate-/r* 35.0%

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

       3. associate-/r/ 35.4%

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

       4. times-frac 38.1%

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

       5. associate-/r* 40.9%

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

       6. sub-div 41.5%

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

       7. *-commutative 41.5%

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

   12. Applied egg-rr 41.5%

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

   if 4.89999999999999968e-214 < b

   1. Initial program 97.7%

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

      1. associate-*r/ 97.7%

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

      2. sub-neg 97.7%

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

      3. exp-sum 81.3%

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

      4. associate-/l* 81.3%

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

      5. associate-/r/ 75.6%

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

      6. exp-neg 75.6%

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

      7. associate-*r/ 75.6%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in t around 0 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*l* 68.8%

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

      3. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in y around 0 61.8%

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

   8. Taylor expanded in b around 0 43.3%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.9 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 17: 37.6% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.4e+72) (/ (- (* x b)) (* y a)) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.4e+72) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a + (a * 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 <= (-9.4d+72)) then
        tmp = -(x * b) / (y * a)
    else
        tmp = x / (y * (a + (a * 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 <= -9.4e+72) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.4e+72:
		tmp = -(x * b) / (y * a)
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.4e+72)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.4e+72)
		tmp = -(x * b) / (y * a);
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.4e+72], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.40000000000000069e72

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 65.6%

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

      4. associate-/l* 65.6%

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

      5. associate-/r/ 65.6%

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

      6. exp-neg 65.6%

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

      7. associate-*r/ 65.6%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*l* 75.5%

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

      3. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. unsub-neg 49.1%

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

      3. associate-/r* 49.1%

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

      4. associate-/l* 38.2%

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

      5. associate-/l* 36.6%

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

   10. Simplified 36.6%

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

   11. Taylor expanded in b around inf 49.1%

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

       1. associate-*r/ 49.1%

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

       2. *-commutative 49.1%

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

       3. neg-mul-1 49.1%

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

   13. Simplified 49.1%

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

   if -9.40000000000000069e72 < b

   1. Initial program 97.7%

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

      1. associate-*r/ 96.9%

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

      2. sub-neg 96.9%

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

      3. exp-sum 84.5%

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

      4. associate-/l* 84.5%

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

      5. associate-/r/ 81.5%

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

      6. exp-neg 81.5%

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

      7. associate-*r/ 81.5%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in t around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-*l* 70.3%

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

      3. *-commutative 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around 0 49.5%

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

   8. Taylor expanded in b around 0 38.1%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 18: 34.3% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.4e+72) (/ (- (* x b)) (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.4e+72) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.4d+72)) then
        tmp = -(x * b) / (y * a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.4e+72) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.4e+72:
		tmp = -(x * b) / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.4e+72)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.4e+72)
		tmp = -(x * b) / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.4e+72], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.40000000000000069e72

   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-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 65.6%

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

      4. associate-/l* 65.6%

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

      5. associate-/r/ 65.6%

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

      6. exp-neg 65.6%

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

      7. associate-*r/ 65.6%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*l* 75.5%

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

      3. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around 0 77.4%

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

   8. Taylor expanded in b around 0 49.1%

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

      1. mul-1-neg 49.1%

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

      2. unsub-neg 49.1%

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

      3. associate-/r* 49.1%

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

      4. associate-/l* 38.2%

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

      5. associate-/l* 36.6%

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

   10. Simplified 36.6%

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

   11. Taylor expanded in b around inf 49.1%

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

       1. associate-*r/ 49.1%

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

       2. *-commutative 49.1%

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

       3. neg-mul-1 49.1%

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

   13. Simplified 49.1%

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

   if -9.40000000000000069e72 < b

   1. Initial program 97.7%

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

      1. associate-*r/ 96.9%

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

      2. sub-neg 96.9%

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

      3. exp-sum 84.5%

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

      4. associate-/l* 84.5%

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

      5. associate-/r/ 81.5%

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

      6. exp-neg 81.5%

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

      7. associate-*r/ 81.5%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in t around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-*l* 70.3%

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

      3. *-commutative 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around 0 49.5%

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

   8. Taylor expanded in b around 0 30.2%

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

      1. *-commutative 30.2%

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

      2. associate-/r* 30.3%

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

   10. Simplified 30.3%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 19: 31.9% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2.9e-166) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.9e-166) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2.9d-166) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.9e-166) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.9e-166:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.9e-166)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.9e-166)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.9e-166], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.9e-166

   1. Initial program 99.5%

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

      1. associate-*r/ 94.9%

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

      2. sub-neg 94.9%

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

      3. exp-sum 80.6%

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

      4. associate-/l* 80.6%

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

      5. associate-/r/ 73.5%

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

      6. exp-neg 73.5%

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

      7. associate-*r/ 73.5%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in t around 0 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*l* 70.2%

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

      3. *-commutative 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in y around 0 46.4%

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

   8. Taylor expanded in b around 0 27.5%

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

      1. *-commutative 27.5%

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

      2. associate-/r* 40.6%

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

   10. Simplified 40.6%

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

   if 2.9e-166 < a

   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-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 79.9%

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

      4. associate-/l* 79.9%

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

      5. associate-/r/ 78.9%

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

      6. exp-neg 78.9%

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

      7. associate-*r/ 78.9%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-*l* 71.9%

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

      3. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in y around 0 58.9%

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

   8. Taylor expanded in b around 0 29.0%

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

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 20: 30.9% 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-*r/ 97.6%

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

   2. sub-neg 97.6%

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

   3. exp-sum 80.0%

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

   4. associate-/l* 80.0%

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

   5. associate-/r/ 77.7%

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

   6. exp-neg 77.7%

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

   7. associate-*r/ 77.7%

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

3. Simplified 70.4%

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

4. Taylor expanded in t around 0 71.6%

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

   1. *-commutative 71.6%

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

   2. associate-*l* 71.6%

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

   3. *-commutative 71.6%

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

6. Simplified 71.6%

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

7. Taylor expanded in y around 0 56.1%

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

8. Taylor expanded in b around 0 28.6%

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

9. Final simplification 28.6%

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

Developer target: 71.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023240 
(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))