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

Percentage Accurate: 98.5% → 98.5%

Time: 22.1s

Alternatives: 24

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

2. Final simplification 98.7%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+44} \lor \neg \left(y \leq 12.6\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.2e+44) (not (<= y 12.6)))
   (/ (* 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 <= -2.2e+44) || !(y <= 12.6)) {
		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 <= (-2.2d+44)) .or. (.not. (y <= 12.6d0))) 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 <= -2.2e+44) || !(y <= 12.6)) {
		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 <= -2.2e+44) or not (y <= 12.6):
		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 <= -2.2e+44) || !(y <= 12.6))
		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 <= -2.2e+44) || ~((y <= 12.6)))
		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, -2.2e+44], N[Not[LessEqual[y, 12.6]], $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 < -2.19999999999999996e44 or 12.5999999999999996 < 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 94.0%

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

      1. mul-1-neg 94.0%

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

   4. Simplified 94.0%

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

   if -2.19999999999999996e44 < y < 12.5999999999999996

   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. Taylor expanded in y around 0 95.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+44} \lor \neg \left(y \leq 12.6\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 76.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ t_2 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq 82000 \lor \neg \left(t \leq 8.8 \cdot 10^{+111}\right) \land t \leq 1.4 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow z y) (* y (* a (exp b))))))
        (t_2 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -4.6e+180)
     t_2
     (if (<= t -1.2e+38)
       t_1
       (if (<= t -4.4e-38)
         (/ (/ (* x (pow a t)) a) y)
         (if (or (<= t 82000.0) (and (not (<= t 8.8e+111)) (<= t 1.4e+163)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(z, y) / (y * (a * exp(b))));
	double t_2 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -4.6e+180) {
		tmp = t_2;
	} else if (t <= -1.2e+38) {
		tmp = t_1;
	} else if (t <= -4.4e-38) {
		tmp = ((x * pow(a, t)) / a) / y;
	} else if ((t <= 82000.0) || (!(t <= 8.8e+111) && (t <= 1.4e+163))) {
		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 * ((z ** y) / (y * (a * exp(b))))
    t_2 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-4.6d+180)) then
        tmp = t_2
    else if (t <= (-1.2d+38)) then
        tmp = t_1
    else if (t <= (-4.4d-38)) then
        tmp = ((x * (a ** t)) / a) / y
    else if ((t <= 82000.0d0) .or. (.not. (t <= 8.8d+111)) .and. (t <= 1.4d+163)) 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(z, y) / (y * (a * Math.exp(b))));
	double t_2 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -4.6e+180) {
		tmp = t_2;
	} else if (t <= -1.2e+38) {
		tmp = t_1;
	} else if (t <= -4.4e-38) {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	} else if ((t <= 82000.0) || (!(t <= 8.8e+111) && (t <= 1.4e+163))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(z, y) / (y * (a * math.exp(b))))
	t_2 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -4.6e+180:
		tmp = t_2
	elif t <= -1.2e+38:
		tmp = t_1
	elif t <= -4.4e-38:
		tmp = ((x * math.pow(a, t)) / a) / y
	elif (t <= 82000.0) or (not (t <= 8.8e+111) and (t <= 1.4e+163)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((z ^ y) / Float64(y * Float64(a * exp(b)))))
	t_2 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -4.6e+180)
		tmp = t_2;
	elseif (t <= -1.2e+38)
		tmp = t_1;
	elseif (t <= -4.4e-38)
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	elseif ((t <= 82000.0) || (!(t <= 8.8e+111) && (t <= 1.4e+163)))
		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 * ((z ^ y) / (y * (a * exp(b))));
	t_2 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -4.6e+180)
		tmp = t_2;
	elseif (t <= -1.2e+38)
		tmp = t_1;
	elseif (t <= -4.4e-38)
		tmp = ((x * (a ^ t)) / a) / y;
	elseif ((t <= 82000.0) || (~((t <= 8.8e+111)) && (t <= 1.4e+163)))
		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[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -4.6e+180], t$95$2, If[LessEqual[t, -1.2e+38], t$95$1, If[LessEqual[t, -4.4e-38], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[t, 82000.0], And[N[Not[LessEqual[t, 8.8e+111]], $MachinePrecision], LessEqual[t, 1.4e+163]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5999999999999998e180 or 82000 < t < 8.79999999999999994e111 or 1.40000000000000007e163 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 89.5%

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

      2. *-commutative 89.5%

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

   3. Simplified 43.4%

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

   4. Taylor expanded in y around 0 69.8%

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

      1. associate-/l* 65.8%

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

      2. sub-neg 65.8%

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

      3. metadata-eval 65.8%

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

      4. associate-/l* 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in b around 0 88.3%

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

   if -4.5999999999999998e180 < t < -1.20000000000000009e38 or -4.40000000000000015e-38 < t < 82000 or 8.79999999999999994e111 < t < 1.40000000000000007e163

   1. Initial program 98.2%

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

      1. associate-*r/ 97.4%

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

      2. sub-neg 97.4%

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

      3. exp-sum 82.1%

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

      4. associate-/l* 82.1%

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

      5. associate-/r/ 80.3%

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

      6. exp-neg 80.3%

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

      7. associate-*r/ 80.3%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in t around 0 84.9%

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

      1. associate-*r* 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*r* 84.9%

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

   6. Simplified 84.9%

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

   if -1.20000000000000009e38 < t < -4.40000000000000015e-38

   1. Initial program 98.5%

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

      1. associate-*l/ 92.3%

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

      2. *-commutative 92.3%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in b around 0 68.1%

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

      1. expm1-log1p-u 61.8%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)\right)}}{y} \]

      2. expm1-udef 50.3%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)} - 1}}{y} \]

      3. *-commutative 50.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \color{blue}{\left(x \cdot {a}^{\left(t - 1\right)}\right)}\right)} - 1}{y} \]

      4. pow-sub 50.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)\right)} - 1}{y} \]

      5. pow1 50.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)\right)} - 1}{y} \]

   6. Applied egg-rr 50.3%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)} - 1}}{y} \]
   7. Step-by-step derivation

      1. expm1-def 62.5%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)\right)}}{y} \]

      2. expm1-log1p 68.8%

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

   8. Simplified 68.8%

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

   9. Taylor expanded in y around 0 87.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq 82000 \lor \neg \left(t \leq 8.8 \cdot 10^{+111}\right) \land t \leq 1.4 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 4: 89.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+119} \lor \neg \left(y \leq 6.2 \cdot 10^{+74}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.35e+119) (not (<= y 6.2e+74)))
   (* 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 <= -2.35e+119) || !(y <= 6.2e+74)) {
		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 <= (-2.35d+119)) .or. (.not. (y <= 6.2d+74))) 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 <= -2.35e+119) || !(y <= 6.2e+74)) {
		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 <= -2.35e+119) or not (y <= 6.2e+74):
		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 <= -2.35e+119) || !(y <= 6.2e+74))
		tmp = Float64(x * Float64(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 <= -2.35e+119) || ~((y <= 6.2e+74)))
		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, -2.35e+119], N[Not[LessEqual[y, 6.2e+74]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $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 < -2.35000000000000004e119 or 6.20000000000000043e74 < 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. 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 78.9%

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

      4. associate-/l* 78.9%

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

      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 58.9%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. associate-*r* 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r* 71.2%

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

   6. Simplified 71.2%

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

   7. Taylor expanded in b around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/r* 88.0%

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

   9. Simplified 88.0%

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

   if -2.35000000000000004e119 < y < 6.20000000000000043e74

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 93.3%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+119} \lor \neg \left(y \leq 6.2 \cdot 10^{+74}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 79.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+115} \lor \neg \left(y \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.5e+115) (not (<= y 2.8e+18)))
   (* x (/ (/ (pow z y) a) y))
   (* (/ (pow a t) a) (/ x (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.5e+115) || !(y <= 2.8e+18)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (pow(a, t) / a) * (x / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.5d+115)) .or. (.not. (y <= 2.8d+18))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = ((a ** t) / a) * (x / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.5e+115) || !(y <= 2.8e+18)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (Math.pow(a, t) / a) * (x / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.5e+115) or not (y <= 2.8e+18):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (math.pow(a, t) / a) * (x / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.5e+115) || !(y <= 2.8e+18))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64((a ^ t) / a) * Float64(x / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.5e+115) || ~((y <= 2.8e+18)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = ((a ^ t) / a) * (x / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.5e+115], N[Not[LessEqual[y, 2.8e+18]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999997e115 or 2.8e18 < 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. 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 75.2%

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

      4. associate-/l* 75.2%

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

      5. associate-/r/ 75.2%

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

      6. exp-neg 75.2%

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

      7. associate-*r/ 75.2%

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

   3. Simplified 58.1%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. associate-*r* 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r* 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in b around 0 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-/r* 85.9%

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

   9. Simplified 85.9%

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

   if -7.4999999999999997e115 < y < 2.8e18

   1. Initial program 97.9%

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

      1. associate-*l/ 90.3%

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

      2. exp-diff 75.1%

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

      3. times-frac 78.7%

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

      4. associate-*l/ 79.1%

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

      5. *-commutative 79.1%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in y around 0 80.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+115} \lor \neg \left(y \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \]

Alternative 6: 79.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+121} \lor \neg \left(y \leq 5.5 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t}}{a}}{\frac{y}{\frac{x}{e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e+121) (not (<= y 5.5e+14)))
   (* x (/ (/ (pow z y) a) y))
   (/ (/ (pow a t) a) (/ y (/ x (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e+121) || !(y <= 5.5e+14)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (pow(a, t) / a) / (y / (x / 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 <= (-8.5d+121)) .or. (.not. (y <= 5.5d+14))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = ((a ** t) / a) / (y / (x / 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 <= -8.5e+121) || !(y <= 5.5e+14)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (Math.pow(a, t) / a) / (y / (x / Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e+121) or not (y <= 5.5e+14):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (math.pow(a, t) / a) / (y / (x / math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e+121) || !(y <= 5.5e+14))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64((a ^ t) / a) / Float64(y / Float64(x / exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e+121) || ~((y <= 5.5e+14)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = ((a ^ t) / a) / (y / (x / exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e+121], N[Not[LessEqual[y, 5.5e+14]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[(y / N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e121 or 5.5e14 < 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. 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 75.2%

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

      4. associate-/l* 75.2%

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

      5. associate-/r/ 75.2%

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

      6. exp-neg 75.2%

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

      7. associate-*r/ 75.2%

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

   3. Simplified 58.1%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. associate-*r* 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r* 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in b around 0 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-/r* 85.9%

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

   9. Simplified 85.9%

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

   if -8.5e121 < y < 5.5e14

   1. Initial program 97.9%

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

      1. associate-*l/ 90.3%

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

      2. *-commutative 90.3%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in y around 0 80.3%

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

      1. associate-/l* 80.7%

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

      2. sub-neg 80.7%

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

      3. metadata-eval 80.7%

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

      4. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

      1. expm1-log1p-u 80.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t + -1\right)}\right)\right)}}{\frac{y}{\frac{x}{e^{b}}}} \]

      2. expm1-udef 70.4%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({a}^{\left(t + -1\right)}\right)} - 1}}{\frac{y}{\frac{x}{e^{b}}}} \]

      3. metadata-eval 70.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({a}^{\left(t + \color{blue}{\left(-1\right)}\right)}\right)} - 1}{\frac{y}{\frac{x}{e^{b}}}} \]

      4. sub-neg 70.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({a}^{\color{blue}{\left(t - 1\right)}}\right)} - 1}{\frac{y}{\frac{x}{e^{b}}}} \]

      5. pow-sub 70.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1}{\frac{y}{\frac{x}{e^{b}}}} \]

      6. pow1 70.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(\frac{{a}^{t}}{\color{blue}{a}}\right)} - 1}{\frac{y}{\frac{x}{e^{b}}}} \]

   8. Applied egg-rr 70.4%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)} - 1}}{\frac{y}{\frac{x}{e^{b}}}} \]
   9. Step-by-step derivation

      1. expm1-def 80.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)\right)}}{\frac{y}{\frac{x}{e^{b}}}} \]

      2. expm1-log1p 80.7%

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

   10. Simplified 80.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+121} \lor \neg \left(y \leq 5.5 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t}}{a}}{\frac{y}{\frac{x}{e^{b}}}}\\ \end{array} \]

Alternative 7: 73.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ t_3 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-220}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y))
        (t_2 (* x (/ (/ (pow z y) a) y)))
        (t_3 (/ x (* a (* y (exp b))))))
   (if (<= y -1.8e+119)
     t_2
     (if (<= y -3.35e-59)
       t_1
       (if (<= y 4.2e-220)
         t_3
         (if (<= y 3.6e-131) t_1 (if (<= y 8.8e+24) 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 + -1.0))) / y;
	double t_2 = x * ((pow(z, y) / a) / y);
	double t_3 = x / (a * (y * exp(b)));
	double tmp;
	if (y <= -1.8e+119) {
		tmp = t_2;
	} else if (y <= -3.35e-59) {
		tmp = t_1;
	} else if (y <= 4.2e-220) {
		tmp = t_3;
	} else if (y <= 3.6e-131) {
		tmp = t_1;
	} else if (y <= 8.8e+24) {
		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 + (-1.0d0)))) / y
    t_2 = x * (((z ** y) / a) / y)
    t_3 = x / (a * (y * exp(b)))
    if (y <= (-1.8d+119)) then
        tmp = t_2
    else if (y <= (-3.35d-59)) then
        tmp = t_1
    else if (y <= 4.2d-220) then
        tmp = t_3
    else if (y <= 3.6d-131) then
        tmp = t_1
    else if (y <= 8.8d+24) 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 + -1.0))) / y;
	double t_2 = x * ((Math.pow(z, y) / a) / y);
	double t_3 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (y <= -1.8e+119) {
		tmp = t_2;
	} else if (y <= -3.35e-59) {
		tmp = t_1;
	} else if (y <= 4.2e-220) {
		tmp = t_3;
	} else if (y <= 3.6e-131) {
		tmp = t_1;
	} else if (y <= 8.8e+24) {
		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 + -1.0))) / y
	t_2 = x * ((math.pow(z, y) / a) / y)
	t_3 = x / (a * (y * math.exp(b)))
	tmp = 0
	if y <= -1.8e+119:
		tmp = t_2
	elif y <= -3.35e-59:
		tmp = t_1
	elif y <= 4.2e-220:
		tmp = t_3
	elif y <= 3.6e-131:
		tmp = t_1
	elif y <= 8.8e+24:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_2 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	t_3 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (y <= -1.8e+119)
		tmp = t_2;
	elseif (y <= -3.35e-59)
		tmp = t_1;
	elseif (y <= 4.2e-220)
		tmp = t_3;
	elseif (y <= 3.6e-131)
		tmp = t_1;
	elseif (y <= 8.8e+24)
		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 + -1.0))) / y;
	t_2 = x * (((z ^ y) / a) / y);
	t_3 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (y <= -1.8e+119)
		tmp = t_2;
	elseif (y <= -3.35e-59)
		tmp = t_1;
	elseif (y <= 4.2e-220)
		tmp = t_3;
	elseif (y <= 3.6e-131)
		tmp = t_1;
	elseif (y <= 8.8e+24)
		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, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+119], t$95$2, If[LessEqual[y, -3.35e-59], t$95$1, If[LessEqual[y, 4.2e-220], t$95$3, If[LessEqual[y, 3.6e-131], t$95$1, If[LessEqual[y, 8.8e+24], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000001e119 or 8.80000000000000007e24 < 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. 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 75.7%

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

      4. associate-/l* 75.7%

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

      5. associate-/r/ 75.7%

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

      6. exp-neg 75.7%

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

      7. associate-*r/ 75.7%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-*r* 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in b around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/r* 86.6%

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

   9. Simplified 86.6%

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

   if -1.80000000000000001e119 < y < -3.35e-59 or 4.19999999999999985e-220 < y < 3.5999999999999999e-131

   1. Initial program 98.8%

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

      1. associate-*l/ 97.2%

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

      2. *-commutative 97.2%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around 0 82.6%

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

      1. associate-/l* 82.6%

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

      2. sub-neg 82.6%

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

      3. metadata-eval 82.6%

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

      4. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in b around 0 84.5%

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

   if -3.35e-59 < y < 4.19999999999999985e-220 or 3.5999999999999999e-131 < y < 8.80000000000000007e24

   1. Initial program 97.3%

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

      1. associate-*l/ 85.6%

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

      2. *-commutative 85.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in y around 0 76.8%

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

      1. associate-/l* 77.5%

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

      2. sub-neg 77.5%

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

      3. metadata-eval 77.5%

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

      4. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in t around 0 81.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 8: 73.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= y -7.2e+115)
     t_1
     (if (<= y -1.35e-58)
       (/ (/ (* x (pow a t)) a) y)
       (if (<= y 1.15e-219)
         t_2
         (if (<= y 1.1e-131)
           (/ (* x (pow a (+ t -1.0))) y)
           (if (<= y 8.8e+24) 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 / (a * (y * exp(b)));
	double tmp;
	if (y <= -7.2e+115) {
		tmp = t_1;
	} else if (y <= -1.35e-58) {
		tmp = ((x * pow(a, t)) / a) / y;
	} else if (y <= 1.15e-219) {
		tmp = t_2;
	} else if (y <= 1.1e-131) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 8.8e+24) {
		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 / (a * (y * exp(b)))
    if (y <= (-7.2d+115)) then
        tmp = t_1
    else if (y <= (-1.35d-58)) then
        tmp = ((x * (a ** t)) / a) / y
    else if (y <= 1.15d-219) then
        tmp = t_2
    else if (y <= 1.1d-131) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 8.8d+24) 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 / (a * (y * Math.exp(b)));
	double tmp;
	if (y <= -7.2e+115) {
		tmp = t_1;
	} else if (y <= -1.35e-58) {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	} else if (y <= 1.15e-219) {
		tmp = t_2;
	} else if (y <= 1.1e-131) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 8.8e+24) {
		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 / (a * (y * math.exp(b)))
	tmp = 0
	if y <= -7.2e+115:
		tmp = t_1
	elif y <= -1.35e-58:
		tmp = ((x * math.pow(a, t)) / a) / y
	elif y <= 1.15e-219:
		tmp = t_2
	elif y <= 1.1e-131:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 8.8e+24:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (y <= -7.2e+115)
		tmp = t_1;
	elseif (y <= -1.35e-58)
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	elseif (y <= 1.15e-219)
		tmp = t_2;
	elseif (y <= 1.1e-131)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 8.8e+24)
		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 / (a * (y * exp(b)));
	tmp = 0.0;
	if (y <= -7.2e+115)
		tmp = t_1;
	elseif (y <= -1.35e-58)
		tmp = ((x * (a ^ t)) / a) / y;
	elseif (y <= 1.15e-219)
		tmp = t_2;
	elseif (y <= 1.1e-131)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 8.8e+24)
		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[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+115], t$95$1, If[LessEqual[y, -1.35e-58], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.15e-219], t$95$2, If[LessEqual[y, 1.1e-131], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.8e+24], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.2000000000000001e115 or 8.80000000000000007e24 < 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. 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 75.7%

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

      4. associate-/l* 75.7%

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

      5. associate-/r/ 75.7%

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

      6. exp-neg 75.7%

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

      7. associate-*r/ 75.7%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-*r* 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in b around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/r* 86.6%

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

   9. Simplified 86.6%

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

   if -7.2000000000000001e115 < y < -1.3499999999999999e-58

   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-*l/ 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in b around 0 66.8%

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

      1. expm1-log1p-u 51.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)\right)}}{y} \]

      2. expm1-udef 51.5%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)} - 1}}{y} \]

      3. *-commutative 51.5%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \color{blue}{\left(x \cdot {a}^{\left(t - 1\right)}\right)}\right)} - 1}{y} \]

      4. pow-sub 51.5%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)\right)} - 1}{y} \]

      5. pow1 51.5%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)\right)} - 1}{y} \]

   6. Applied egg-rr 51.5%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)} - 1}}{y} \]
   7. Step-by-step derivation

      1. expm1-def 51.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)\right)}}{y} \]

      2. expm1-log1p 66.8%

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

   8. Simplified 66.8%

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

   9. Taylor expanded in y around 0 79.6%

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

   if -1.3499999999999999e-58 < y < 1.14999999999999994e-219 or 1.1e-131 < y < 8.80000000000000007e24

   1. Initial program 97.3%

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

      1. associate-*l/ 85.6%

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

      2. *-commutative 85.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in y around 0 76.8%

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

      1. associate-/l* 77.5%

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

      2. sub-neg 77.5%

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

      3. metadata-eval 77.5%

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

      4. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in t around 0 81.4%

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

   if 1.14999999999999994e-219 < y < 1.1e-131

   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-*l/ 93.7%

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

      2. *-commutative 93.7%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in y around 0 83.9%

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

      1. associate-/l* 79.8%

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

      2. sub-neg 79.8%

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

      3. metadata-eval 79.8%

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

      4. associate-/l* 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in b around 0 92.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-219}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 9: 74.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+83} \lor \neg \left(b \leq 2.95 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.8e+83) (not (<= b 2.95e+54)))
   (/ x (* a (* y (exp b))))
   (* x (/ (/ (pow z y) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.8e+83) || !(b <= 2.95e+54)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * ((pow(z, y) / 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 <= (-2.8d+83)) .or. (.not. (b <= 2.95d+54))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (((z ** y) / 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 <= -2.8e+83) || !(b <= 2.95e+54)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.8e+83) or not (b <= 2.95e+54):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.8e+83) || !(b <= 2.95e+54))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.8e+83) || ~((b <= 2.95e+54)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.8e+83], N[Not[LessEqual[b, 2.95e+54]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8e83 or 2.9499999999999999e54 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 85.1%

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

      2. *-commutative 85.1%

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

   3. Simplified 41.6%

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

   4. Taylor expanded in y around 0 58.5%

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

      1. associate-/l* 63.4%

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

      2. sub-neg 63.4%

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

      3. metadata-eval 63.4%

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

      4. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in t around 0 84.4%

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

   if -2.8e83 < b < 2.9499999999999999e54

   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/ 96.5%

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

      2. sub-neg 96.5%

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

      3. exp-sum 90.7%

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

      4. associate-/l* 90.7%

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

      5. associate-/r/ 90.1%

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

      6. exp-neg 90.1%

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

      7. associate-*r/ 90.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in t around 0 69.7%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in b around 0 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-/r* 74.3%

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

   9. Simplified 74.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+83} \lor \neg \left(b \leq 2.95 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 10: 59.7% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. associate-*l/ 86.9%

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

   2. *-commutative 86.9%

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

3. Simplified 62.1%

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

4. Taylor expanded in y around 0 63.9%

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

   1. associate-/l* 64.1%

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

   2. sub-neg 64.1%

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

   3. metadata-eval 64.1%

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

   4. associate-/l* 64.1%

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

6. Simplified 64.1%

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

7. Taylor expanded in t around 0 60.9%

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

8. Final simplification 60.9%

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

Alternative 11: 40.3% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.6e+49)
   (/ (* x (/ (- b) a)) y)
   (if (<= b 5e-293)
     (/ 1.0 (/ (* y a) x))
     (if (<= b 3.1e-186) (/ (/ x a) y) (/ x (* y (* a (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e+49) {
		tmp = (x * (-b / a)) / y;
	} else if (b <= 5e-293) {
		tmp = 1.0 / ((y * a) / x);
	} else if (b <= 3.1e-186) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * (1.0 + 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 <= (-7.6d+49)) then
        tmp = (x * (-b / a)) / y
    else if (b <= 5d-293) then
        tmp = 1.0d0 / ((y * a) / x)
    else if (b <= 3.1d-186) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (a * (1.0d0 + 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 <= -7.6e+49) {
		tmp = (x * (-b / a)) / y;
	} else if (b <= 5e-293) {
		tmp = 1.0 / ((y * a) / x);
	} else if (b <= 3.1e-186) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.6e+49:
		tmp = (x * (-b / a)) / y
	elif b <= 5e-293:
		tmp = 1.0 / ((y * a) / x)
	elif b <= 3.1e-186:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.6e+49)
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	elseif (b <= 5e-293)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	elseif (b <= 3.1e-186)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.6e+49)
		tmp = (x * (-b / a)) / y;
	elseif (b <= 5e-293)
		tmp = 1.0 / ((y * a) / x);
	elseif (b <= 3.1e-186)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.6e+49], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5e-293], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-186], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.5999999999999997e49

   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 90.3%

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

      1. mul-1-neg 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. exp-neg 84.6%

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

      2. associate-*l/ 84.6%

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

      3. *-lft-identity 84.6%

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

      4. exp-sum 84.6%

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

      5. rem-exp-log 84.6%

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

      6. *-commutative 84.6%

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

      7. associate-/r* 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in b around 0 39.2%

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

   9. Taylor expanded in b around inf 39.2%

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

       1. mul-1-neg 39.2%

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

       2. *-commutative 39.2%

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

       3. associate-*r/ 43.0%

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

       4. *-commutative 43.0%

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

       5. distribute-rgt-neg-in 43.0%

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

   11. Simplified 43.0%

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

   if -7.5999999999999997e49 < b < 5.0000000000000003e-293

   1. Initial program 97.4%

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

      1. associate-*r/ 98.6%

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

      2. sub-neg 98.6%

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

      3. exp-sum 97.3%

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

      4. associate-/l* 97.3%

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

      5. associate-/r/ 97.3%

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

      6. exp-neg 97.3%

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

      7. associate-*r/ 97.3%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around 0 72.2%

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

      1. associate-*r* 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-*r* 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in b around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-/r* 75.0%

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

   9. Simplified 75.0%

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

   10. Taylor expanded in y around 0 45.1%

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

       1. associate-*r/ 45.0%

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

       2. clear-num 45.8%

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

       3. *-commutative 45.8%

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

       4. *-rgt-identity 45.8%

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

   12. Applied egg-rr 45.8%

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

   if 5.0000000000000003e-293 < b < 3.10000000000000009e-186

   1. Initial program 97.5%

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

      1. associate-*l/ 93.2%

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

      2. *-commutative 93.2%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. associate-/l* 73.9%

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

      2. sub-neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. associate-/l* 73.9%

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

   6. Simplified 73.9%

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

   7. Taylor expanded in t around 0 29.1%

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

   8. Taylor expanded in b around 0 29.1%

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

      1. associate-/r* 45.4%

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

   10. Simplified 45.4%

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

   if 3.10000000000000009e-186 < b

   1. Initial program 99.4%

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

      1. associate-*l/ 83.2%

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

      2. *-commutative 83.2%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in y around 0 55.7%

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

      1. associate-/l* 57.9%

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

      2. sub-neg 57.9%

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

      3. metadata-eval 57.9%

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

      4. associate-/l* 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in t around 0 63.7%

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

   8. Taylor expanded in b around 0 37.1%

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

   9. Taylor expanded in y around 0 38.9%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 12: 40.0% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(\left(-\frac{-1}{a}\right) - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6e-262)
   (/ (* x (- (- (/ -1.0 a)) (/ b a))) y)
   (if (<= b 3.1e-275)
     (/ (/ (* x (- b)) a) y)
     (if (<= b 9.2e-186) (/ (/ x a) y) (/ x (* y (* a (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e-262) {
		tmp = (x * (-(-1.0 / a) - (b / a))) / y;
	} else if (b <= 3.1e-275) {
		tmp = ((x * -b) / a) / y;
	} else if (b <= 9.2e-186) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * (1.0 + 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 <= (-6d-262)) then
        tmp = (x * (-((-1.0d0) / a) - (b / a))) / y
    else if (b <= 3.1d-275) then
        tmp = ((x * -b) / a) / y
    else if (b <= 9.2d-186) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (a * (1.0d0 + 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 <= -6e-262) {
		tmp = (x * (-(-1.0 / a) - (b / a))) / y;
	} else if (b <= 3.1e-275) {
		tmp = ((x * -b) / a) / y;
	} else if (b <= 9.2e-186) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6e-262:
		tmp = (x * (-(-1.0 / a) - (b / a))) / y
	elif b <= 3.1e-275:
		tmp = ((x * -b) / a) / y
	elif b <= 9.2e-186:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6e-262)
		tmp = Float64(Float64(x * Float64(Float64(-Float64(-1.0 / a)) - Float64(b / a))) / y);
	elseif (b <= 3.1e-275)
		tmp = Float64(Float64(Float64(x * Float64(-b)) / a) / y);
	elseif (b <= 9.2e-186)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6e-262)
		tmp = (x * (-(-1.0 / a) - (b / a))) / y;
	elseif (b <= 3.1e-275)
		tmp = ((x * -b) / a) / y;
	elseif (b <= 9.2e-186)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6e-262], N[(N[(x * N[((-N[(-1.0 / a), $MachinePrecision]) - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.1e-275], N[(N[(N[(x * (-b)), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 9.2e-186], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.00000000000000036e-262

   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. Taylor expanded in t around 0 79.8%

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

      1. mul-1-neg 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. exp-neg 63.4%

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

      2. associate-*l/ 63.4%

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

      3. *-lft-identity 63.4%

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

      4. exp-sum 64.2%

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

      5. rem-exp-log 64.8%

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

      6. *-commutative 64.8%

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

      7. associate-/r* 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in b around 0 41.5%

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

   9. Taylor expanded in x around -inf 43.2%

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

       1. associate-*r/ 43.2%

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

       2. mul-1-neg 43.2%

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

       3. distribute-rgt-neg-in 43.2%

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

       4. unpow-1 43.2%

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

       5. sub-neg 43.2%

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

       6. unpow-1 43.2%

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

       7. distribute-neg-frac 43.2%

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

       8. metadata-eval 43.2%

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

   11. Simplified 43.2%

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

   if -6.00000000000000036e-262 < b < 3.1e-275

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0 70.8%

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

      1. mul-1-neg 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in y around 0 18.8%

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

      1. exp-neg 18.8%

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

      2. associate-*l/ 18.8%

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

      3. *-lft-identity 18.8%

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

      4. exp-sum 18.8%

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

      5. rem-exp-log 18.8%

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

      6. *-commutative 18.8%

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

      7. associate-/r* 18.8%

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

   7. Simplified 18.8%

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

   8. Taylor expanded in b around 0 18.8%

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

   9. Taylor expanded in b around inf 54.8%

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

   if 3.1e-275 < b < 9.2000000000000003e-186

   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-*l/ 92.4%

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

      2. *-commutative 92.4%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around 0 69.0%

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

      1. associate-/l* 69.0%

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

      2. sub-neg 69.0%

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

      3. metadata-eval 69.0%

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

      4. associate-/l* 69.0%

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

   6. Simplified 69.0%

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

   7. Taylor expanded in t around 0 29.3%

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

   8. Taylor expanded in b around 0 29.3%

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

      1. associate-/r* 48.7%

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

   10. Simplified 48.7%

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

   if 9.2000000000000003e-186 < b

   1. Initial program 99.4%

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

      1. associate-*l/ 83.2%

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

      2. *-commutative 83.2%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in y around 0 55.7%

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

      1. associate-/l* 57.9%

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

      2. sub-neg 57.9%

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

      3. metadata-eval 57.9%

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

      4. associate-/l* 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in t around 0 63.7%

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

   8. Taylor expanded in b around 0 37.1%

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

   9. Taylor expanded in y around 0 38.9%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot \left(\left(-\frac{-1}{a}\right) - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 13: 39.7% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{a \cdot \left(x - x \cdot b\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+32)
   (/ (/ (* a (- x (* x b))) (* a a)) y)
   (if (<= b 7.2e-293)
     (/ 1.0 (/ (* y a) x))
     (if (<= b 2.25e-185) (/ (/ x a) y) (/ x (* y (* a (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+32) {
		tmp = ((a * (x - (x * b))) / (a * a)) / y;
	} else if (b <= 7.2e-293) {
		tmp = 1.0 / ((y * a) / x);
	} else if (b <= 2.25e-185) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * (1.0 + 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 <= (-1.25d+32)) then
        tmp = ((a * (x - (x * b))) / (a * a)) / y
    else if (b <= 7.2d-293) then
        tmp = 1.0d0 / ((y * a) / x)
    else if (b <= 2.25d-185) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (a * (1.0d0 + 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 <= -1.25e+32) {
		tmp = ((a * (x - (x * b))) / (a * a)) / y;
	} else if (b <= 7.2e-293) {
		tmp = 1.0 / ((y * a) / x);
	} else if (b <= 2.25e-185) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+32:
		tmp = ((a * (x - (x * b))) / (a * a)) / y
	elif b <= 7.2e-293:
		tmp = 1.0 / ((y * a) / x)
	elif b <= 2.25e-185:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+32)
		tmp = Float64(Float64(Float64(a * Float64(x - Float64(x * b))) / Float64(a * a)) / y);
	elseif (b <= 7.2e-293)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	elseif (b <= 2.25e-185)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+32)
		tmp = ((a * (x - (x * b))) / (a * a)) / y;
	elseif (b <= 7.2e-293)
		tmp = 1.0 / ((y * a) / x);
	elseif (b <= 2.25e-185)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+32], N[(N[(N[(a * N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.2e-293], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e-185], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.2499999999999999e32

   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 88.9%

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

      1. mul-1-neg 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in y around 0 83.3%

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

      1. exp-neg 83.3%

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

      2. associate-*l/ 83.3%

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

      3. *-lft-identity 83.3%

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

      4. exp-sum 83.3%

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

      5. rem-exp-log 83.3%

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

      6. *-commutative 83.3%

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

      7. associate-/r* 72.0%

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

   7. Simplified 72.0%

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

   8. Taylor expanded in b around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. frac-add 46.6%

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

      3. neg-mul-1 46.6%

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

      4. distribute-rgt-neg-in 46.6%

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

   10. Applied egg-rr 46.6%

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

       1. +-commutative 46.6%

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

       2. *-commutative 46.6%

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

       3. distribute-lft-out 46.6%

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

       4. distribute-rgt-neg-out 46.6%

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

       5. *-commutative 46.6%

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

       6. unsub-neg 46.6%

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

   12. Simplified 46.6%

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

   if -1.2499999999999999e32 < b < 7.1999999999999997e-293

   1. Initial program 97.3%

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

      1. associate-*r/ 98.6%

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

      2. sub-neg 98.6%

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

      3. exp-sum 98.6%

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

      4. associate-/l* 98.6%

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

      5. associate-/r/ 98.6%

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

      6. exp-neg 98.6%

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

      7. associate-*r/ 98.6%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in t around 0 72.8%

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

      1. associate-*r* 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-*r* 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in b around 0 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-/r* 75.6%

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

   9. Simplified 75.6%

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

   10. Taylor expanded in y around 0 44.9%

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

       1. associate-*r/ 44.8%

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

       2. clear-num 45.6%

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

       3. *-commutative 45.6%

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

       4. *-rgt-identity 45.6%

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

   12. Applied egg-rr 45.6%

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

   if 7.1999999999999997e-293 < b < 2.2500000000000001e-185

   1. Initial program 97.5%

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

      1. associate-*l/ 93.2%

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

      2. *-commutative 93.2%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. associate-/l* 73.9%

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

      2. sub-neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. associate-/l* 73.9%

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

   6. Simplified 73.9%

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

   7. Taylor expanded in t around 0 29.1%

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

   8. Taylor expanded in b around 0 29.1%

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

      1. associate-/r* 45.4%

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

   10. Simplified 45.4%

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

   if 2.2500000000000001e-185 < b

   1. Initial program 99.4%

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

      1. associate-*l/ 83.2%

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

      2. *-commutative 83.2%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in y around 0 55.7%

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

      1. associate-/l* 57.9%

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

      2. sub-neg 57.9%

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

      3. metadata-eval 57.9%

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

      4. associate-/l* 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in t around 0 63.7%

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

   8. Taylor expanded in b around 0 37.1%

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

   9. Taylor expanded in y around 0 38.9%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{a \cdot \left(x - x \cdot b\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 14: 39.3% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{b}{a} \cdot \frac{-x}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+83)
   (* (/ b a) (/ (- x) y))
   (if (<= b 2.8e+54) (/ 1.0 (/ (* y a) x)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+83) {
		tmp = (b / a) * (-x / y);
	} else if (b <= 2.8e+54) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (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 <= (-2.5d+83)) then
        tmp = (b / a) * (-x / y)
    else if (b <= 2.8d+54) then
        tmp = 1.0d0 / ((y * a) / x)
    else
        tmp = x / (y * (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 <= -2.5e+83) {
		tmp = (b / a) * (-x / y);
	} else if (b <= 2.8e+54) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+83:
		tmp = (b / a) * (-x / y)
	elif b <= 2.8e+54:
		tmp = 1.0 / ((y * a) / x)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+83)
		tmp = Float64(Float64(b / a) * Float64(Float64(-x) / y));
	elseif (b <= 2.8e+54)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+83)
		tmp = (b / a) * (-x / y);
	elseif (b <= 2.8e+54)
		tmp = 1.0 / ((y * a) / x);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+83], N[(N[(b / a), $MachinePrecision] * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+54], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.50000000000000014e83

   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 93.3%

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

      1. mul-1-neg 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. exp-neg 86.6%

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

      2. associate-*l/ 86.6%

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

      3. *-lft-identity 86.6%

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

      4. exp-sum 86.6%

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

      5. rem-exp-log 86.6%

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

      6. *-commutative 86.6%

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

      7. associate-/r* 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in b around 0 40.6%

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

   9. Taylor expanded in b around inf 36.3%

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

       1. associate-*r/ 36.3%

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

       2. mul-1-neg 36.3%

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

       3. distribute-rgt-neg-out 36.3%

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

       4. *-commutative 36.3%

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

       5. times-frac 42.6%

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

   11. Simplified 42.6%

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

   if -2.50000000000000014e83 < b < 2.80000000000000015e54

   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/ 96.5%

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

      2. sub-neg 96.5%

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

      3. exp-sum 90.7%

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

      4. associate-/l* 90.7%

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

      5. associate-/r/ 90.1%

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

      6. exp-neg 90.1%

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

      7. associate-*r/ 90.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in t around 0 69.7%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in b around 0 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-/r* 74.3%

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

   9. Simplified 74.3%

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

   10. Taylor expanded in y around 0 38.1%

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

       1. associate-*r/ 38.1%

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

       2. clear-num 38.5%

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

       3. *-commutative 38.5%

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

       4. *-rgt-identity 38.5%

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

   12. Applied egg-rr 38.5%

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

   if 2.80000000000000015e54 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. associate-/l* 63.3%

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

      2. sub-neg 63.3%

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

      3. metadata-eval 63.3%

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

      4. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in t around 0 82.7%

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

   8. Taylor expanded in b around 0 39.0%

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

   9. Taylor expanded in b around -inf 42.3%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{b}{a} \cdot \frac{-x}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 15: 39.2% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(-b\right)}{y}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e+50)
   (/ (* (/ x a) (- b)) y)
   (if (<= b 1.05e+55) (/ 1.0 (/ (* y a) x)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+50) {
		tmp = ((x / a) * -b) / y;
	} else if (b <= 1.05e+55) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (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 <= (-1.55d+50)) then
        tmp = ((x / a) * -b) / y
    else if (b <= 1.05d+55) then
        tmp = 1.0d0 / ((y * a) / x)
    else
        tmp = x / (y * (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 <= -1.55e+50) {
		tmp = ((x / a) * -b) / y;
	} else if (b <= 1.05e+55) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e+50:
		tmp = ((x / a) * -b) / y
	elif b <= 1.05e+55:
		tmp = 1.0 / ((y * a) / x)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.55e+50)
		tmp = Float64(Float64(Float64(x / a) * Float64(-b)) / y);
	elseif (b <= 1.05e+55)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.55e+50)
		tmp = ((x / a) * -b) / y;
	elseif (b <= 1.05e+55)
		tmp = 1.0 / ((y * a) / x);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.55e+50], N[(N[(N[(x / a), $MachinePrecision] * (-b)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.05e+55], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.55000000000000001e50

   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 90.3%

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

      1. mul-1-neg 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. exp-neg 84.6%

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

      2. associate-*l/ 84.6%

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

      3. *-lft-identity 84.6%

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

      4. exp-sum 84.6%

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

      5. rem-exp-log 84.6%

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

      6. *-commutative 84.6%

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

      7. associate-/r* 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in b around 0 39.2%

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

   9. Taylor expanded in b around inf 39.2%

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

       1. mul-1-neg 39.2%

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

       2. associate-*r/ 39.1%

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

       3. distribute-rgt-neg-in 39.1%

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

   11. Simplified 39.1%

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

   if -1.55000000000000001e50 < b < 1.05e55

   1. Initial program 97.8%

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

      1. associate-*r/ 96.4%

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

      2. sub-neg 96.4%

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

      3. exp-sum 92.3%

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

      4. associate-/l* 92.3%

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

      5. associate-/r/ 91.6%

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

      6. exp-neg 91.6%

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

      7. associate-*r/ 91.7%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around 0 69.6%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*r* 69.6%

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

   6. Simplified 69.6%

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

   7. Taylor expanded in b around 0 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/r* 73.7%

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

   9. Simplified 73.7%

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

   10. Taylor expanded in y around 0 39.1%

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

       1. associate-*r/ 39.1%

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

       2. clear-num 39.5%

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

       3. *-commutative 39.5%

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

       4. *-rgt-identity 39.5%

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

   12. Applied egg-rr 39.5%

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

   if 1.05e55 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. associate-/l* 63.3%

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

      2. sub-neg 63.3%

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

      3. metadata-eval 63.3%

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

      4. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in t around 0 82.7%

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

   8. Taylor expanded in b around 0 39.0%

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

   9. Taylor expanded in b around -inf 42.3%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(-b\right)}{y}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 16: 40.2% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.2e+49)
   (/ (* x (/ (- b) a)) y)
   (if (<= b 5.8e+54) (/ 1.0 (/ (* y a) x)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.2e+49) {
		tmp = (x * (-b / a)) / y;
	} else if (b <= 5.8e+54) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (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 <= (-4.2d+49)) then
        tmp = (x * (-b / a)) / y
    else if (b <= 5.8d+54) then
        tmp = 1.0d0 / ((y * a) / x)
    else
        tmp = x / (y * (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 <= -4.2e+49) {
		tmp = (x * (-b / a)) / y;
	} else if (b <= 5.8e+54) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.2e+49:
		tmp = (x * (-b / a)) / y
	elif b <= 5.8e+54:
		tmp = 1.0 / ((y * a) / x)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.2e+49)
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	elseif (b <= 5.8e+54)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.2e+49)
		tmp = (x * (-b / a)) / y;
	elseif (b <= 5.8e+54)
		tmp = 1.0 / ((y * a) / x);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.2e+49], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.8e+54], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.20000000000000022e49

   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 90.3%

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

      1. mul-1-neg 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. exp-neg 84.6%

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

      2. associate-*l/ 84.6%

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

      3. *-lft-identity 84.6%

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

      4. exp-sum 84.6%

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

      5. rem-exp-log 84.6%

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

      6. *-commutative 84.6%

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

      7. associate-/r* 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in b around 0 39.2%

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

   9. Taylor expanded in b around inf 39.2%

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

       1. mul-1-neg 39.2%

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

       2. *-commutative 39.2%

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

       3. associate-*r/ 43.0%

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

       4. *-commutative 43.0%

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

       5. distribute-rgt-neg-in 43.0%

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

   11. Simplified 43.0%

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

   if -4.20000000000000022e49 < b < 5.7999999999999997e54

   1. Initial program 97.8%

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

      1. associate-*r/ 96.4%

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

      2. sub-neg 96.4%

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

      3. exp-sum 92.3%

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

      4. associate-/l* 92.3%

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

      5. associate-/r/ 91.6%

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

      6. exp-neg 91.6%

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

      7. associate-*r/ 91.7%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around 0 69.6%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*r* 69.6%

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

   6. Simplified 69.6%

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

   7. Taylor expanded in b around 0 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/r* 73.7%

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

   9. Simplified 73.7%

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

   10. Taylor expanded in y around 0 39.1%

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

       1. associate-*r/ 39.1%

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

       2. clear-num 39.5%

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

       3. *-commutative 39.5%

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

       4. *-rgt-identity 39.5%

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

   12. Applied egg-rr 39.5%

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

   if 5.7999999999999997e54 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. associate-/l* 63.3%

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

      2. sub-neg 63.3%

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

      3. metadata-eval 63.3%

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

      4. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in t around 0 82.7%

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

   8. Taylor expanded in b around 0 39.0%

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

   9. Taylor expanded in b around -inf 42.3%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 17: 40.1% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -15500:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -15500.0) (/ (* x (/ (- b) a)) y) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -15500.0) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-15500.0d0)) then
        tmp = (x * (-b / a)) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -15500.0) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -15500.0:
		tmp = (x * (-b / a)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -15500.0)
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -15500.0)
		tmp = (x * (-b / a)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -15500.0], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -15500

   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 89.8%

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

      1. mul-1-neg 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. exp-neg 84.7%

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

      2. associate-*l/ 84.7%

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

      3. *-lft-identity 84.7%

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

      4. exp-sum 84.7%

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

      5. rem-exp-log 84.7%

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

      6. *-commutative 84.7%

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

      7. associate-/r* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in b around 0 41.5%

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

   9. Taylor expanded in b around inf 41.5%

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

       1. mul-1-neg 41.5%

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

       2. *-commutative 41.5%

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

       3. associate-*r/ 44.8%

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

       4. *-commutative 44.8%

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

       5. distribute-rgt-neg-in 44.8%

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

   11. Simplified 44.8%

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

   if -15500 < b

   1. Initial program 98.4%

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

      1. associate-*l/ 86.6%

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

      2. *-commutative 86.6%

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

   3. Simplified 67.1%

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

   4. Taylor expanded in y around 0 64.4%

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

      1. associate-/l* 64.2%

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

      2. sub-neg 64.2%

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

      3. metadata-eval 64.2%

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

      4. associate-/l* 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in t around 0 53.9%

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

   8. Taylor expanded in b around 0 38.4%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -15500:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 18: 31.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5.5e-197) (/ (/ x y) a) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.5e-197) {
		tmp = (x / y) / a;
	} else {
		tmp = x * (1.0 / (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 <= 5.5d-197) then
        tmp = (x / y) / a
    else
        tmp = x * (1.0d0 / (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 <= 5.5e-197) {
		tmp = (x / y) / a;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5.5e-197:
		tmp = (x / y) / a
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5.5e-197)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5.5e-197)
		tmp = (x / y) / a;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5.5e-197], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.50000000000000037e-197

   1. Initial program 99.1%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in b around 0 58.4%

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

      1. expm1-log1p-u 41.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)\right)}}{y} \]

      2. expm1-udef 40.0%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)} - 1}}{y} \]

      3. *-commutative 40.0%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \color{blue}{\left(x \cdot {a}^{\left(t - 1\right)}\right)}\right)} - 1}{y} \]

      4. pow-sub 40.0%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)\right)} - 1}{y} \]

      5. pow1 40.0%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)\right)} - 1}{y} \]

   6. Applied egg-rr 40.0%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)} - 1}}{y} \]
   7. Step-by-step derivation

      1. expm1-def 41.6%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)\right)}}{y} \]

      2. expm1-log1p 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in y around 0 59.4%

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

   10. Taylor expanded in t around 0 25.8%

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

       1. associate-/r* 38.5%

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

   12. Simplified 38.5%

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

   if 5.50000000000000037e-197 < a

   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/ 99.2%

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

      2. sub-neg 99.2%

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

      3. exp-sum 80.4%

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

      4. associate-/l* 80.4%

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

      5. associate-/r/ 80.4%

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

      6. exp-neg 80.4%

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

      7. associate-*r/ 80.4%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in t around 0 69.3%

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

      1. associate-*r* 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-*r* 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in b around 0 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/r* 62.3%

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

   9. Simplified 62.3%

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

   10. Taylor expanded in y around 0 33.2%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]

Alternative 19: 32.2% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 3e+35) (/ 1.0 (/ a (/ x y))) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 3e+35) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x * (1.0 / (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 <= 3d+35) then
        tmp = 1.0d0 / (a / (x / y))
    else
        tmp = x * (1.0d0 / (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 <= 3e+35) {
		tmp = 1.0 / (a / (x / y));
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 3e+35:
		tmp = 1.0 / (a / (x / y))
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 3e+35)
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 3e+35)
		tmp = 1.0 / (a / (x / y));
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 3e+35], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.99999999999999991e35

   1. Initial program 99.4%

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

      1. associate-*r/ 97.1%

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

      2. sub-neg 97.1%

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

      3. exp-sum 74.7%

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

      4. associate-/l* 74.7%

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

      5. associate-/r/ 72.6%

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

      6. exp-neg 72.6%

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

      7. associate-*r/ 72.6%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-*r* 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*r* 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in b around 0 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-/r* 62.5%

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

   9. Simplified 62.5%

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

   10. Taylor expanded in y around 0 30.4%

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

       1. div-inv 30.4%

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

       2. associate-/r* 35.7%

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

       3. clear-num 36.0%

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

   12. Applied egg-rr 36.0%

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

   if 2.99999999999999991e35 < 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/ 98.9%

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

      2. sub-neg 98.9%

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

      3. exp-sum 82.1%

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

      4. associate-/l* 82.1%

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

      5. associate-/r/ 82.1%

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

      6. exp-neg 82.1%

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

      7. associate-*r/ 82.1%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in t around 0 66.9%

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

      1. associate-*r* 63.4%

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

      2. *-commutative 63.4%

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

      3. associate-*r* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in b around 0 49.9%

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

      1. *-commutative 49.9%

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

      2. associate-/r* 58.7%

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

   9. Simplified 58.7%

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

   10. Taylor expanded in y around 0 32.9%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]

Alternative 20: 31.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 5.8e+54) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.8e+54) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 5.8d+54) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.8e+54) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.8e+54:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.8e+54)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 5.8e+54)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.8e+54], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.7999999999999997e54

   1. Initial program 98.4%

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

      1. associate-*l/ 89.0%

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

      2. *-commutative 89.0%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. associate-/l* 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

      4. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in t around 0 64.6%

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

   8. Taylor expanded in b around 0 32.7%

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

      1. associate-/r* 35.3%

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

   10. Simplified 35.3%

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

   if 5.7999999999999997e54 < 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. Step-by-step derivation

      1. associate-*l/ 79.7%

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

      2. *-commutative 79.7%

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

   3. Simplified 44.1%

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

   4. Taylor expanded in y around 0 39.7%

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

      1. associate-/l* 38.0%

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

      2. sub-neg 38.0%

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

      3. metadata-eval 38.0%

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

      4. associate-/l* 38.0%

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

   6. Simplified 38.0%

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

   7. Taylor expanded in t around 0 48.6%

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

   8. Taylor expanded in b around 0 38.7%

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

   9. Taylor expanded in b around inf 36.7%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 21: 35.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5e+54) (/ (/ x a) y) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e+54) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (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 <= 5d+54) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (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 <= 5e+54) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5e+54:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5e+54)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5e+54)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5e+54], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.00000000000000005e54

   1. Initial program 98.4%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in y around 0 66.1%

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

      1. associate-/l* 64.3%

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

      2. sub-neg 64.3%

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

      3. metadata-eval 64.3%

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

      4. associate-/l* 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in t around 0 54.6%

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

   8. Taylor expanded in b around 0 33.3%

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

      1. associate-/r* 34.1%

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

   10. Simplified 34.1%

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

   if 5.00000000000000005e54 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. associate-/l* 63.3%

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

      2. sub-neg 63.3%

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

      3. metadata-eval 63.3%

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

      4. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in t around 0 82.7%

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

   8. Taylor expanded in b around 0 39.0%

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

   9. Taylor expanded in b around -inf 42.3%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 22: 32.5% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.4e-106) (/ (/ 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 <= 1.4e-106) {
		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 <= 1.4d-106) 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 <= 1.4e-106) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.4e-106:
		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 <= 1.4e-106)
		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 <= 1.4e-106)
		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, 1.4e-106], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.39999999999999994e-106

   1. Initial program 99.3%

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

      1. associate-*l/ 86.6%

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

      2. *-commutative 86.6%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in y around 0 58.6%

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

      1. associate-/l* 62.0%

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

      2. sub-neg 62.0%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{y \cdot e^{b}}{x}} \]

      3. metadata-eval 62.0%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{y \cdot e^{b}}{x}} \]

      4. associate-/l* 62.0%

         \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\color{blue}{\frac{y}{\frac{x}{e^{b}}}}} \]

   6. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{y}{\frac{x}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 59.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 27.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. associate-/r* 35.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   10. Simplified 35.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

   if 1.39999999999999994e-106 < a

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\left({a}^{\left(t - 1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 66.6%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]
   5. Step-by-step derivation

      1. associate-/l* 65.2%

         \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y \cdot e^{b}}{x}}} \]

      2. sub-neg 65.2%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{y \cdot e^{b}}{x}} \]

      3. metadata-eval 65.2%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{y \cdot e^{b}}{x}} \]

      4. associate-/l* 65.2%

         \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\color{blue}{\frac{y}{\frac{x}{e^{b}}}}} \]

   6. Simplified 65.2%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{y}{\frac{x}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 61.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 33.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 33.6%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 33.6%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.4 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 23: 31.6% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.6e-193) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.6e-193) {
		tmp = (x / y) / a;
	} 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 <= 1.6d-193) then
        tmp = (x / y) / a
    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 <= 1.6e-193) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.6e-193:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.6e-193)
		tmp = Float64(Float64(x / y) / a);
	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 <= 1.6e-193)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.6e-193], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.60000000000000003e-193

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. Simplified 55.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t - 1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in b around 0 57.5%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)}{y}} \]
   5. Step-by-step derivation

      1. expm1-log1p-u 40.8%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)\right)}}{y} \]

      2. expm1-udef 39.3%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left({a}^{\left(t - 1\right)} \cdot x\right)\right)} - 1}}{y} \]

      3. *-commutative 39.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \color{blue}{\left(x \cdot {a}^{\left(t - 1\right)}\right)}\right)} - 1}{y} \]

      4. pow-sub 39.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)\right)} - 1}{y} \]

      5. pow1 39.3%

         \[\leadsto \frac{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)\right)} - 1}{y} \]

   6. Applied egg-rr 39.3%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)} - 1}}{y} \]
   7. Step-by-step derivation

      1. expm1-def 40.9%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)\right)\right)}}{y} \]

      2. expm1-log1p 57.7%

         \[\leadsto \frac{\color{blue}{{z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)}}{y} \]

   8. Simplified 57.7%

      \[\leadsto \frac{\color{blue}{{z}^{y} \cdot \left(x \cdot \frac{{a}^{t}}{a}\right)}}{y} \]

   9. Taylor expanded in y around 0 58.4%

      \[\leadsto \frac{\color{blue}{\frac{{a}^{t} \cdot x}{a}}}{y} \]

   10. Taylor expanded in t around 0 25.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   11. Step-by-step derivation

       1. associate-/r* 37.9%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   12. Simplified 37.9%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   if 1.60000000000000003e-193 < a

   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-*l/ 86.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 86.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. Simplified 64.1%

      \[\leadsto \color{blue}{\left({a}^{\left(t - 1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in y around 0 66.4%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]
   5. Step-by-step derivation

      1. associate-/l* 65.7%

         \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y \cdot e^{b}}{x}}} \]

      2. sub-neg 65.7%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{y \cdot e^{b}}{x}} \]

      3. metadata-eval 65.7%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{y \cdot e^{b}}{x}} \]

      4. associate-/l* 65.7%

         \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\color{blue}{\frac{y}{\frac{x}{e^{b}}}}} \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{y}{\frac{x}{e^{b}}}}} \]

   7. Taylor expanded in t around 0 61.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 33.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   10. Simplified 33.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 24: 31.0% 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 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 86.9%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. *-commutative 86.9%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

3. Simplified 62.1%

   \[\leadsto \color{blue}{\left({a}^{\left(t - 1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

4. Taylor expanded in y around 0 63.9%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]
5. Step-by-step derivation

   1. associate-/l* 64.1%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y \cdot e^{b}}{x}}} \]

   2. sub-neg 64.1%

      \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{y \cdot e^{b}}{x}} \]

   3. metadata-eval 64.1%

      \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{y \cdot e^{b}}{x}} \]

   4. associate-/l* 64.1%

      \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\color{blue}{\frac{y}{\frac{x}{e^{b}}}}} \]

6. Simplified 64.1%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{y}{\frac{x}{e^{b}}}}} \]

7. Taylor expanded in t around 0 60.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

8. Taylor expanded in b around 0 31.5%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
9. Step-by-step derivation

   1. *-commutative 31.5%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

10. Simplified 31.5%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

11. Final simplification 31.5%

    \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 71.8% 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 2023196 
(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))