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

Percentage Accurate: 98.4% → 98.4%

Time: 33.0s

Alternatives: 21

Speedup: 1.0×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

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: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -500000000 \lor \neg \left(t + -1 \leq -0.999999999\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -500000000.0) (not (<= (+ t -1.0) -0.999999999)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -500000000.0) || !((t + -1.0) <= -0.999999999)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-500000000.0d0)) .or. (.not. ((t + (-1.0d0)) <= (-0.999999999d0)))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -500000000.0) || !((t + -1.0) <= -0.999999999)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -500000000.0) or not ((t + -1.0) <= -0.999999999):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -500000000.0) || !(Float64(t + -1.0) <= -0.999999999))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -500000000.0) || ~(((t + -1.0) <= -0.999999999)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -500000000.0], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.999999999]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -5e8 or -0.999999999000000028 < (-.f64 t 1)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.7%

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

   if -5e8 < (-.f64 t 1) < -0.999999999000000028

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 97.2%

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

      1. +-commutative 97.2%

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

      2. mul-1-neg 97.2%

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

      3. unsub-neg 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -500000000 \lor \neg \left(t + -1 \leq -0.999999999\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{1}{a}}{e^{b} \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 19\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -1.26e+75)
     t_1
     (if (<= t -6.4e+65)
       (/ (/ 1.0 a) (* (exp b) (/ y x)))
       (if (or (<= t -1.85e-7) (not (<= t 19.0)))
         t_1
         (/ (* x (pow z y)) (* a (* y (exp b)))))))))

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 tmp;
	if (t <= -1.26e+75) {
		tmp = t_1;
	} else if (t <= -6.4e+65) {
		tmp = (1.0 / a) / (exp(b) * (y / x));
	} else if ((t <= -1.85e-7) || !(t <= 19.0)) {
		tmp = t_1;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-1.26d+75)) then
        tmp = t_1
    else if (t <= (-6.4d+65)) then
        tmp = (1.0d0 / a) / (exp(b) * (y / x))
    else if ((t <= (-1.85d-7)) .or. (.not. (t <= 19.0d0))) then
        tmp = t_1
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -1.26e+75) {
		tmp = t_1;
	} else if (t <= -6.4e+65) {
		tmp = (1.0 / a) / (Math.exp(b) * (y / x));
	} else if ((t <= -1.85e-7) || !(t <= 19.0)) {
		tmp = t_1;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -1.26e+75:
		tmp = t_1
	elif t <= -6.4e+65:
		tmp = (1.0 / a) / (math.exp(b) * (y / x))
	elif (t <= -1.85e-7) or not (t <= 19.0):
		tmp = t_1
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -1.26e+75)
		tmp = t_1;
	elseif (t <= -6.4e+65)
		tmp = Float64(Float64(1.0 / a) / Float64(exp(b) * Float64(y / x)));
	elseif ((t <= -1.85e-7) || !(t <= 19.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -1.26e+75)
		tmp = t_1;
	elseif (t <= -6.4e+65)
		tmp = (1.0 / a) / (exp(b) * (y / x));
	elseif ((t <= -1.85e-7) || ~((t <= 19.0)))
		tmp = t_1;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	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]}, If[LessEqual[t, -1.26e+75], t$95$1, If[LessEqual[t, -6.4e+65], N[(N[(1.0 / a), $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.85e-7], N[Not[LessEqual[t, 19.0]], $MachinePrecision]], t$95$1, N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.26000000000000003e75 or -6.40000000000000014e65 < t < -1.85000000000000002e-7 or 19 < 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. Taylor expanded in y around 0 94.9%

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

   3. Taylor expanded in b around 0 87.6%

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

      1. exp-to-pow 87.6%

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

      2. sub-neg 87.6%

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

      3. metadata-eval 87.6%

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

      4. +-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -1.26000000000000003e75 < t < -6.40000000000000014e65

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. exp-diff 50.0%

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

      4. associate-/l/ 50.0%

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

      5. exp-sum 0.0%

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

      6. *-commutative 0.0%

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

      7. exp-to-pow 0.0%

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

      8. *-commutative 0.0%

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

      9. exp-to-pow 0.0%

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

      10. sub-neg 0.0%

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

      11. metadata-eval 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   5. Taylor expanded in y around 0 83.6%

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

   if -1.85000000000000002e-7 < t < 19

   1. Initial program 97.2%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

      3. +-commutative 83.7%

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

      4. associate--l+ 83.7%

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

      5. exp-sum 83.7%

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

      6. *-commutative 83.7%

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

      7. exp-to-pow 84.3%

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

      8. sub-neg 84.3%

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

      9. metadata-eval 84.3%

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

      10. exp-diff 76.5%

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

      11. *-commutative 76.5%

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

      12. exp-to-pow 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in t around 0 87.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+75}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{1}{a}}{e^{b} \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 19\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 4: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a}}{e^{b} \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 88\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -1.26e+75)
     t_1
     (if (<= t -4.8e+66)
       (/ (/ (pow z y) a) (* (exp b) (/ y x)))
       (if (or (<= t -1.85e-7) (not (<= t 88.0)))
         t_1
         (/ (* x (pow z y)) (* a (* y (exp b)))))))))

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 tmp;
	if (t <= -1.26e+75) {
		tmp = t_1;
	} else if (t <= -4.8e+66) {
		tmp = (pow(z, y) / a) / (exp(b) * (y / x));
	} else if ((t <= -1.85e-7) || !(t <= 88.0)) {
		tmp = t_1;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-1.26d+75)) then
        tmp = t_1
    else if (t <= (-4.8d+66)) then
        tmp = ((z ** y) / a) / (exp(b) * (y / x))
    else if ((t <= (-1.85d-7)) .or. (.not. (t <= 88.0d0))) then
        tmp = t_1
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -1.26e+75) {
		tmp = t_1;
	} else if (t <= -4.8e+66) {
		tmp = (Math.pow(z, y) / a) / (Math.exp(b) * (y / x));
	} else if ((t <= -1.85e-7) || !(t <= 88.0)) {
		tmp = t_1;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -1.26e+75:
		tmp = t_1
	elif t <= -4.8e+66:
		tmp = (math.pow(z, y) / a) / (math.exp(b) * (y / x))
	elif (t <= -1.85e-7) or not (t <= 88.0):
		tmp = t_1
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -1.26e+75)
		tmp = t_1;
	elseif (t <= -4.8e+66)
		tmp = Float64(Float64((z ^ y) / a) / Float64(exp(b) * Float64(y / x)));
	elseif ((t <= -1.85e-7) || !(t <= 88.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -1.26e+75)
		tmp = t_1;
	elseif (t <= -4.8e+66)
		tmp = ((z ^ y) / a) / (exp(b) * (y / x));
	elseif ((t <= -1.85e-7) || ~((t <= 88.0)))
		tmp = t_1;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	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]}, If[LessEqual[t, -1.26e+75], t$95$1, If[LessEqual[t, -4.8e+66], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.85e-7], N[Not[LessEqual[t, 88.0]], $MachinePrecision]], t$95$1, N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.26000000000000003e75 or -4.8000000000000003e66 < t < -1.85000000000000002e-7 or 88 < 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. Taylor expanded in y around 0 94.9%

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

   3. Taylor expanded in b around 0 87.6%

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

      1. exp-to-pow 87.6%

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

      2. sub-neg 87.6%

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

      3. metadata-eval 87.6%

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

      4. +-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -1.26000000000000003e75 < t < -4.8000000000000003e66

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. exp-diff 50.0%

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

      4. associate-/l/ 50.0%

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

      5. exp-sum 0.0%

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

      6. *-commutative 0.0%

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

      7. exp-to-pow 0.0%

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

      8. *-commutative 0.0%

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

      9. exp-to-pow 0.0%

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

      10. sub-neg 0.0%

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

      11. metadata-eval 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -1.85000000000000002e-7 < t < 88

   1. Initial program 97.2%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

      3. +-commutative 83.7%

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

      4. associate--l+ 83.7%

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

      5. exp-sum 83.7%

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

      6. *-commutative 83.7%

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

      7. exp-to-pow 84.3%

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

      8. sub-neg 84.3%

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

      9. metadata-eval 84.3%

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

      10. exp-diff 76.5%

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

      11. *-commutative 76.5%

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

      12. exp-to-pow 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in t around 0 87.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+75}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a}}{e^{b} \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 88\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 5: 85.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 1.9 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.85e-7) (not (<= t 1.9e-39)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e-7) || !(t <= 1.9e-39)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.85d-7)) .or. (.not. (t <= 1.9d-39))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e-7) || !(t <= 1.9e-39)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.85e-7) or not (t <= 1.9e-39):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.85e-7) || !(t <= 1.9e-39))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.85e-7) || ~((t <= 1.9e-39)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.85e-7], N[Not[LessEqual[t, 1.9e-39]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85000000000000002e-7 or 1.9000000000000001e-39 < 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. Taylor expanded in y around 0 93.4%

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

   if -1.85000000000000002e-7 < t < 1.9000000000000001e-39

   1. Initial program 97.0%

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

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. +-commutative 83.6%

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

      4. associate--l+ 83.6%

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

      5. exp-sum 83.6%

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

      6. *-commutative 83.6%

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

      7. exp-to-pow 84.2%

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

      8. sub-neg 84.2%

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

      9. metadata-eval 84.2%

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

      10. exp-diff 75.9%

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

      11. *-commutative 75.9%

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

      12. exp-to-pow 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around 0 87.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 1.9 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 6: 82.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+46} \lor \neg \left(y \leq 1.06 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e+46) (not (<= y 1.06e+96)))
   (/ x (/ a (/ (pow z y) y)))
   (/ x (/ y (/ (pow a (+ t -1.0)) (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e+46) || !(y <= 1.06e+96)) {
		tmp = x / (a / (pow(z, y) / y));
	} else {
		tmp = x / (y / (pow(a, (t + -1.0)) / 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 <= (-1d+46)) .or. (.not. (y <= 1.06d+96))) then
        tmp = x / (a / ((z ** y) / y))
    else
        tmp = x / (y / ((a ** (t + (-1.0d0))) / 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 <= -1e+46) || !(y <= 1.06e+96)) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else {
		tmp = x / (y / (Math.pow(a, (t + -1.0)) / Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e+46) or not (y <= 1.06e+96):
		tmp = x / (a / (math.pow(z, y) / y))
	else:
		tmp = x / (y / (math.pow(a, (t + -1.0)) / math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e+46) || !(y <= 1.06e+96))
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	else
		tmp = Float64(x / Float64(y / Float64((a ^ Float64(t + -1.0)) / exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1e+46) || ~((y <= 1.06e+96)))
		tmp = x / (a / ((z ^ y) / y));
	else
		tmp = x / (y / ((a ^ (t + -1.0)) / exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e+46], N[Not[LessEqual[y, 1.06e+96]], $MachinePrecision]], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999999e45 or 1.06e96 < 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/ 81.6%

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

      2. *-commutative 81.6%

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

      3. +-commutative 81.6%

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

      4. associate--l+ 81.6%

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

      5. exp-sum 60.2%

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

      6. *-commutative 60.2%

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

      7. exp-to-pow 60.2%

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

      8. sub-neg 60.2%

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

      9. metadata-eval 60.2%

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

      10. exp-diff 46.9%

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

      11. *-commutative 46.9%

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

      12. exp-to-pow 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in b around 0 66.4%

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

      1. associate-/l* 66.4%

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

      2. *-commutative 66.4%

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

      3. exp-to-pow 66.4%

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

      4. *-commutative 66.4%

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

      5. exp-sum 91.0%

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

      6. exp-sum 66.4%

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

      7. *-commutative 66.4%

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

      8. exp-to-pow 66.4%

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

      9. *-commutative 66.4%

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

      10. exp-to-pow 66.4%

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

      11. sub-neg 66.4%

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

      12. metadata-eval 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in t around 0 70.7%

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

      1. associate-/l* 79.9%

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

   9. Simplified 79.9%

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

   if -9.9999999999999999e45 < y < 1.06e96

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 95.7%

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

      1. associate-/l* 97.8%

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

      2. div-exp 86.4%

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

      3. exp-to-pow 86.8%

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

      4. sub-neg 86.8%

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

      5. metadata-eval 86.8%

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

   4. Simplified 86.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+46} \lor \neg \left(y \leq 1.06 \cdot 10^{+96}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\\ \end{array} \]

Alternative 7: 75.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_3 := \frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y))
        (t_2 (/ x (* a (* y (exp b)))))
        (t_3 (/ x (/ a (/ (pow z y) y)))))
   (if (<= b -6.5e+21)
     t_2
     (if (<= b -5.7e-70)
       t_1
       (if (<= b -2.4e-114)
         t_3
         (if (<= b 2.1e-235) t_1 (if (<= b 1.06e+21) 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 / (a * (y * exp(b)));
	double t_3 = x / (a / (pow(z, y) / y));
	double tmp;
	if (b <= -6.5e+21) {
		tmp = t_2;
	} else if (b <= -5.7e-70) {
		tmp = t_1;
	} else if (b <= -2.4e-114) {
		tmp = t_3;
	} else if (b <= 2.1e-235) {
		tmp = t_1;
	} else if (b <= 1.06e+21) {
		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 / (a * (y * exp(b)))
    t_3 = x / (a / ((z ** y) / y))
    if (b <= (-6.5d+21)) then
        tmp = t_2
    else if (b <= (-5.7d-70)) then
        tmp = t_1
    else if (b <= (-2.4d-114)) then
        tmp = t_3
    else if (b <= 2.1d-235) then
        tmp = t_1
    else if (b <= 1.06d+21) 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 / (a * (y * Math.exp(b)));
	double t_3 = x / (a / (Math.pow(z, y) / y));
	double tmp;
	if (b <= -6.5e+21) {
		tmp = t_2;
	} else if (b <= -5.7e-70) {
		tmp = t_1;
	} else if (b <= -2.4e-114) {
		tmp = t_3;
	} else if (b <= 2.1e-235) {
		tmp = t_1;
	} else if (b <= 1.06e+21) {
		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 / (a * (y * math.exp(b)))
	t_3 = x / (a / (math.pow(z, y) / y))
	tmp = 0
	if b <= -6.5e+21:
		tmp = t_2
	elif b <= -5.7e-70:
		tmp = t_1
	elif b <= -2.4e-114:
		tmp = t_3
	elif b <= 2.1e-235:
		tmp = t_1
	elif b <= 1.06e+21:
		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(a * Float64(y * exp(b))))
	t_3 = Float64(x / Float64(a / Float64((z ^ y) / y)))
	tmp = 0.0
	if (b <= -6.5e+21)
		tmp = t_2;
	elseif (b <= -5.7e-70)
		tmp = t_1;
	elseif (b <= -2.4e-114)
		tmp = t_3;
	elseif (b <= 2.1e-235)
		tmp = t_1;
	elseif (b <= 1.06e+21)
		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 / (a * (y * exp(b)));
	t_3 = x / (a / ((z ^ y) / y));
	tmp = 0.0;
	if (b <= -6.5e+21)
		tmp = t_2;
	elseif (b <= -5.7e-70)
		tmp = t_1;
	elseif (b <= -2.4e-114)
		tmp = t_3;
	elseif (b <= 2.1e-235)
		tmp = t_1;
	elseif (b <= 1.06e+21)
		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[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+21], t$95$2, If[LessEqual[b, -5.7e-70], t$95$1, If[LessEqual[b, -2.4e-114], t$95$3, If[LessEqual[b, 2.1e-235], t$95$1, If[LessEqual[b, 1.06e+21], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.5e21 or 1.06e21 < 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. Taylor expanded in y around 0 92.9%

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

      1. associate-/l* 92.9%

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

      2. div-exp 73.7%

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

      3. exp-to-pow 73.7%

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

      4. sub-neg 73.7%

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

      5. metadata-eval 73.7%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in t around 0 84.3%

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

   if -6.5e21 < b < -5.70000000000000028e-70 or -2.4000000000000001e-114 < b < 2.1000000000000001e-235

   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. Taylor expanded in y around 0 77.5%

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

   3. Taylor expanded in b around 0 77.5%

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

      1. exp-to-pow 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. +-commutative 77.6%

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

   5. Simplified 77.6%

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

   if -5.70000000000000028e-70 < b < -2.4000000000000001e-114 or 2.1000000000000001e-235 < b < 1.06e21

   1. Initial program 96.4%

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

      1. associate-*l/ 85.8%

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

      2. *-commutative 85.8%

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

      3. +-commutative 85.8%

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

      4. associate--l+ 85.8%

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

      5. exp-sum 72.2%

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

      6. *-commutative 72.2%

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

      7. exp-to-pow 72.9%

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

      8. sub-neg 72.9%

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

      9. metadata-eval 72.9%

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

      10. exp-diff 72.9%

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

      11. *-commutative 72.9%

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

      12. exp-to-pow 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in b around 0 82.9%

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

      1. associate-/l* 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-to-pow 85.4%

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

      4. *-commutative 85.4%

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

      5. exp-sum 99.0%

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

      6. exp-sum 85.4%

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

      7. *-commutative 85.4%

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

      8. exp-to-pow 85.4%

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

      9. *-commutative 85.4%

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

      10. exp-to-pow 85.9%

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

      11. sub-neg 85.9%

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

      12. metadata-eval 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in t around 0 77.9%

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

      1. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-235}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 59.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b)))))
        (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -1.75e-54)
     t_2
     (if (<= b 6e-254)
       t_1
       (if (<= b 6.2e-232)
         (/ (- b) (* y (/ a x)))
         (if (<= b 1.05e-172) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double t_2 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -1.75e-54) {
		tmp = t_2;
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 1.05e-172) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-1.75d-54)) then
        tmp = t_2
    else if (b <= 6d-254) then
        tmp = t_1
    else if (b <= 6.2d-232) then
        tmp = -b / (y * (a / x))
    else if (b <= 1.05d-172) 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 / ((a * 0.5) * (y * (b * b)));
	double t_2 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -1.75e-54) {
		tmp = t_2;
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 1.05e-172) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	t_2 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -1.75e-54:
		tmp = t_2
	elif b <= 6e-254:
		tmp = t_1
	elif b <= 6.2e-232:
		tmp = -b / (y * (a / x))
	elif b <= 1.05e-172:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -1.75e-54)
		tmp = t_2;
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif (b <= 1.05e-172)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	t_2 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -1.75e-54)
		tmp = t_2;
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = -b / (y * (a / x));
	elseif (b <= 1.05e-172)
		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[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e-54], t$95$2, If[LessEqual[b, 6e-254], t$95$1, If[LessEqual[b, 6.2e-232], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-172], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.74999999999999991e-54 or 1.05e-172 < b

   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. Taylor expanded in y around 0 85.9%

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

      1. associate-/l* 86.3%

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

      2. div-exp 71.3%

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

      3. exp-to-pow 71.4%

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

      4. sub-neg 71.4%

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

      5. metadata-eval 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in t around 0 71.3%

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

   if -1.74999999999999991e-54 < b < 6.00000000000000023e-254 or 6.1999999999999998e-232 < b < 1.05e-172

   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. Taylor expanded in y around 0 68.5%

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

      1. associate-/l* 73.1%

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

      2. div-exp 73.1%

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

      3. exp-to-pow 73.5%

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

      4. sub-neg 73.5%

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

      5. metadata-eval 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in t around 0 28.3%

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

   6. Taylor expanded in b around 0 28.3%

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

      1. +-commutative 28.3%

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

      2. associate-*r* 28.3%

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

      3. distribute-rgt-out 28.3%

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

      4. unpow2 28.3%

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

   8. Simplified 28.3%

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

   9. Taylor expanded in b around inf 48.0%

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

       1. associate-*r* 48.0%

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

       2. *-commutative 48.0%

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

       3. unpow2 48.0%

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

   11. Simplified 48.0%

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

   if 6.00000000000000023e-254 < b < 6.1999999999999998e-232

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 9: 75.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0031 \lor \neg \left(y \leq 14600000000000\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0031) (not (<= y 14600000000000.0)))
   (/ x (/ a (/ (pow z y) y)))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0031) || !(y <= 14600000000000.0)) {
		tmp = x / (a / (pow(z, y) / y));
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-0.0031d0)) .or. (.not. (y <= 14600000000000.0d0))) then
        tmp = x / (a / ((z ** y) / y))
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.0031) || !(y <= 14600000000000.0)) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.0031) or not (y <= 14600000000000.0):
		tmp = x / (a / (math.pow(z, y) / y))
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.0031) || !(y <= 14600000000000.0))
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.0031) || ~((y <= 14600000000000.0)))
		tmp = x / (a / ((z ^ y) / y));
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.0031], N[Not[LessEqual[y, 14600000000000.0]], $MachinePrecision]], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00309999999999999989 or 1.46e13 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 84.7%

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

      2. *-commutative 84.7%

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

      3. +-commutative 84.7%

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

      4. associate--l+ 84.7%

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

      5. exp-sum 60.1%

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

      6. *-commutative 60.1%

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

      7. exp-to-pow 60.2%

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

      8. sub-neg 60.2%

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

      9. metadata-eval 60.2%

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

      10. exp-diff 49.1%

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

      11. *-commutative 49.1%

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

      12. exp-to-pow 49.1%

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

   3. Simplified 49.1%

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

   4. Taylor expanded in b around 0 65.3%

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

      1. associate-/l* 65.3%

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

      2. *-commutative 65.3%

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

      3. exp-to-pow 65.3%

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

      4. *-commutative 65.3%

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

      5. exp-sum 92.4%

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

      6. exp-sum 65.3%

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

      7. *-commutative 65.3%

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

      8. exp-to-pow 65.3%

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

      9. *-commutative 65.3%

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

      10. exp-to-pow 65.3%

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

      11. sub-neg 65.3%

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

      12. metadata-eval 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in t around 0 68.9%

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

      1. associate-/l* 76.6%

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

   9. Simplified 76.6%

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

   if -0.00309999999999999989 < y < 1.46e13

   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 97.7%

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

      1. associate-/l* 99.5%

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

      2. div-exp 86.5%

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

      3. exp-to-pow 86.9%

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

      4. sub-neg 86.9%

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

      5. metadata-eval 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in t around 0 70.9%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0031 \lor \neg \left(y \leq 14600000000000\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 10: 45.7% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -5.4e+80)
     (- (/ x (* y a)) (/ (* x (/ b y)) a))
     (if (<= b 6e-254)
       t_1
       (if (<= b 9e-232)
         (/ (- b) (* y (/ a x)))
         (if (<= b 2.3e-172)
           t_1
           (/ x (* a (+ y (* y (+ b (* 0.5 (* b b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -5.4e+80) {
		tmp = (x / (y * a)) - ((x * (b / y)) / a);
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 9e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 2.3e-172) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-5.4d+80)) then
        tmp = (x / (y * a)) - ((x * (b / y)) / a)
    else if (b <= 6d-254) then
        tmp = t_1
    else if (b <= 9d-232) then
        tmp = -b / (y * (a / x))
    else if (b <= 2.3d-172) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * (b + (0.5d0 * (b * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -5.4e+80) {
		tmp = (x / (y * a)) - ((x * (b / y)) / a);
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 9e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 2.3e-172) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -5.4e+80:
		tmp = (x / (y * a)) - ((x * (b / y)) / a)
	elif b <= 6e-254:
		tmp = t_1
	elif b <= 9e-232:
		tmp = -b / (y * (a / x))
	elif b <= 2.3e-172:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -5.4e+80)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x * Float64(b / y)) / a));
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 9e-232)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif (b <= 2.3e-172)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b + Float64(0.5 * Float64(b * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -5.4e+80)
		tmp = (x / (y * a)) - ((x * (b / y)) / a);
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 9e-232)
		tmp = -b / (y * (a / x));
	elseif (b <= 2.3e-172)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e+80], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-254], t$95$1, If[LessEqual[b, 9e-232], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-172], t$95$1, N[(x / N[(a * N[(y + N[(y * N[(b + N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.39999999999999966e80

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. associate-/l* 95.2%

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

      2. div-exp 68.4%

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

      3. exp-to-pow 68.4%

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

      4. sub-neg 68.4%

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

      5. metadata-eval 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around 0 90.4%

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

   6. Taylor expanded in b around 0 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

      4. *-commutative 48.1%

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

      5. times-frac 45.6%

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

   8. Simplified 45.6%

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

      1. associate-*l/ 55.3%

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

   10. Applied egg-rr 55.3%

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

   if -5.39999999999999966e80 < b < 6.00000000000000023e-254 or 8.99999999999999933e-232 < b < 2.29999999999999995e-172

   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. Taylor expanded in y around 0 69.9%

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

      1. associate-/l* 73.3%

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

      2. div-exp 71.3%

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

      3. exp-to-pow 71.7%

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

      4. sub-neg 71.7%

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

      5. metadata-eval 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in t around 0 33.2%

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

   6. Taylor expanded in b around 0 27.5%

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

      1. +-commutative 27.5%

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

      2. associate-*r* 27.5%

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

      3. distribute-rgt-out 28.5%

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

      4. unpow2 28.5%

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

   8. Simplified 28.5%

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

   9. Taylor expanded in b around inf 43.2%

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

       1. associate-*r* 43.2%

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

       2. *-commutative 43.2%

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

       3. unpow2 43.2%

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

   11. Simplified 43.2%

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

   if 6.00000000000000023e-254 < b < 8.99999999999999933e-232

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 2.29999999999999995e-172 < b

   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 85.2%

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

      1. associate-/l* 86.0%

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

      2. div-exp 73.7%

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

      3. exp-to-pow 73.9%

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

      4. sub-neg 73.9%

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

      5. metadata-eval 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around 0 69.6%

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

   6. Taylor expanded in b around 0 56.8%

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

      1. +-commutative 56.8%

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

      2. associate-*r* 56.8%

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

      3. distribute-rgt-out 56.8%

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

      4. unpow2 56.8%

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

   8. Simplified 56.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \]

Alternative 11: 46.0% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(x \cdot \frac{b}{y}\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -3.3e+109)
     (/ (- (* a (/ x a)) (* y (* x (/ b y)))) (* y a))
     (if (<= b 6e-254)
       t_1
       (if (<= b 6.2e-232)
         (/ (- b) (* y (/ a x)))
         (if (<= b 1.45e-171)
           t_1
           (/ x (* a (+ y (* y (+ b (* 0.5 (* b b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -3.3e+109) {
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a);
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 1.45e-171) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-3.3d+109)) then
        tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a)
    else if (b <= 6d-254) then
        tmp = t_1
    else if (b <= 6.2d-232) then
        tmp = -b / (y * (a / x))
    else if (b <= 1.45d-171) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * (b + (0.5d0 * (b * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -3.3e+109) {
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a);
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 1.45e-171) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -3.3e+109:
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a)
	elif b <= 6e-254:
		tmp = t_1
	elif b <= 6.2e-232:
		tmp = -b / (y * (a / x))
	elif b <= 1.45e-171:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -3.3e+109)
		tmp = Float64(Float64(Float64(a * Float64(x / a)) - Float64(y * Float64(x * Float64(b / y)))) / Float64(y * a));
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif (b <= 1.45e-171)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b + Float64(0.5 * Float64(b * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -3.3e+109)
		tmp = ((a * (x / a)) - (y * (x * (b / y)))) / (y * a);
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = -b / (y * (a / x));
	elseif (b <= 1.45e-171)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+109], N[(N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-254], t$95$1, If[LessEqual[b, 6.2e-232], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-171], t$95$1, N[(x / N[(a * N[(y + N[(y * N[(b + N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.2999999999999999e109

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

      1. associate-/l* 97.2%

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

      2. div-exp 68.6%

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

      3. exp-to-pow 68.6%

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

      4. sub-neg 68.6%

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

      5. metadata-eval 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in t around 0 94.4%

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

   6. Taylor expanded in b around 0 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

      5. times-frac 50.0%

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

   8. Simplified 50.0%

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

      1. associate-/r* 50.0%

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

      2. associate-*l/ 58.7%

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

      3. frac-sub 66.6%

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

   10. Applied egg-rr 66.6%

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

   if -3.2999999999999999e109 < b < 6.00000000000000023e-254 or 6.1999999999999998e-232 < b < 1.4499999999999999e-171

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 70.6%

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

      1. associate-/l* 73.8%

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

      2. div-exp 71.1%

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

      3. exp-to-pow 71.4%

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

      4. sub-neg 71.4%

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

      5. metadata-eval 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in t around 0 35.1%

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

   6. Taylor expanded in b around 0 27.0%

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

      1. +-commutative 27.0%

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

      2. associate-*r* 27.0%

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

      3. distribute-rgt-out 28.9%

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

      4. unpow2 28.9%

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

   8. Simplified 28.9%

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

   9. Taylor expanded in b around inf 42.7%

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

       1. associate-*r* 42.7%

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

       2. *-commutative 42.7%

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

       3. unpow2 42.7%

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

   11. Simplified 42.7%

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

   if 6.00000000000000023e-254 < b < 6.1999999999999998e-232

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 1.4499999999999999e-171 < b

   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 85.2%

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

      1. associate-/l* 86.0%

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

      2. div-exp 73.7%

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

      3. exp-to-pow 73.9%

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

      4. sub-neg 73.9%

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

      5. metadata-eval 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around 0 69.6%

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

   6. Taylor expanded in b around 0 56.8%

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

      1. +-commutative 56.8%

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

      2. associate-*r* 56.8%

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

      3. distribute-rgt-out 56.8%

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

      4. unpow2 56.8%

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

   8. Simplified 56.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(x \cdot \frac{b}{y}\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \]

Alternative 12: 47.6% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot \left(b \cdot 0.5\right)\right) \cdot \frac{\frac{x}{y}}{a} + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -1.55e+82)
     (+ (* (* b (* b 0.5)) (/ (/ x y) a)) (/ (- x (* x b)) (* y a)))
     (if (<= b 6e-254)
       t_1
       (if (<= b 9e-232)
         (/ (- b) (* y (/ a x)))
         (if (<= b 1.08e-172)
           t_1
           (/ x (* a (+ y (* y (+ b (* 0.5 (* b b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -1.55e+82) {
		tmp = ((b * (b * 0.5)) * ((x / y) / a)) + ((x - (x * b)) / (y * a));
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 9e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 1.08e-172) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-1.55d+82)) then
        tmp = ((b * (b * 0.5d0)) * ((x / y) / a)) + ((x - (x * b)) / (y * a))
    else if (b <= 6d-254) then
        tmp = t_1
    else if (b <= 9d-232) then
        tmp = -b / (y * (a / x))
    else if (b <= 1.08d-172) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * (b + (0.5d0 * (b * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -1.55e+82) {
		tmp = ((b * (b * 0.5)) * ((x / y) / a)) + ((x - (x * b)) / (y * a));
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 9e-232) {
		tmp = -b / (y * (a / x));
	} else if (b <= 1.08e-172) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -1.55e+82:
		tmp = ((b * (b * 0.5)) * ((x / y) / a)) + ((x - (x * b)) / (y * a))
	elif b <= 6e-254:
		tmp = t_1
	elif b <= 9e-232:
		tmp = -b / (y * (a / x))
	elif b <= 1.08e-172:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -1.55e+82)
		tmp = Float64(Float64(Float64(b * Float64(b * 0.5)) * Float64(Float64(x / y) / a)) + Float64(Float64(x - Float64(x * b)) / Float64(y * a)));
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 9e-232)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif (b <= 1.08e-172)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * Float64(b + Float64(0.5 * Float64(b * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -1.55e+82)
		tmp = ((b * (b * 0.5)) * ((x / y) / a)) + ((x - (x * b)) / (y * a));
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 9e-232)
		tmp = -b / (y * (a / x));
	elseif (b <= 1.08e-172)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * (b + (0.5 * (b * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+82], N[(N[(N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-254], t$95$1, If[LessEqual[b, 9e-232], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.08e-172], t$95$1, N[(x / N[(a * N[(y + N[(y * N[(b + N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55000000000000016e82

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. associate-/l* 95.2%

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

      2. div-exp 68.4%

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

      3. exp-to-pow 68.4%

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

      4. sub-neg 68.4%

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

      5. metadata-eval 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around 0 90.4%

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

   6. Taylor expanded in b around 0 6.2%

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

      1. +-commutative 6.2%

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

      2. associate-*r* 6.2%

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

      3. distribute-rgt-out 11.4%

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

      4. unpow2 11.4%

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

   8. Simplified 11.4%

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

   9. Taylor expanded in b around 0 42.2%

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

   11. Simplified 64.1%

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

   if -1.55000000000000016e82 < b < 6.00000000000000023e-254 or 8.99999999999999933e-232 < b < 1.08e-172

   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. Taylor expanded in y around 0 69.9%

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

      1. associate-/l* 73.3%

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

      2. div-exp 71.3%

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

      3. exp-to-pow 71.7%

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

      4. sub-neg 71.7%

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

      5. metadata-eval 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in t around 0 33.2%

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

   6. Taylor expanded in b around 0 27.5%

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

      1. +-commutative 27.5%

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

      2. associate-*r* 27.5%

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

      3. distribute-rgt-out 28.5%

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

      4. unpow2 28.5%

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

   8. Simplified 28.5%

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

   9. Taylor expanded in b around inf 43.2%

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

       1. associate-*r* 43.2%

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

       2. *-commutative 43.2%

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

       3. unpow2 43.2%

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

   11. Simplified 43.2%

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

   if 6.00000000000000023e-254 < b < 8.99999999999999933e-232

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 1.08e-172 < b

   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 85.2%

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

      1. associate-/l* 86.0%

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

      2. div-exp 73.7%

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

      3. exp-to-pow 73.9%

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

      4. sub-neg 73.9%

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

      5. metadata-eval 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in t around 0 69.6%

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

   6. Taylor expanded in b around 0 56.8%

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

      1. +-commutative 56.8%

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

      2. associate-*r* 56.8%

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

      3. distribute-rgt-out 56.8%

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

      4. unpow2 56.8%

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

   8. Simplified 56.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot \left(b \cdot 0.5\right)\right) \cdot \frac{\frac{x}{y}}{a} + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}\\ \end{array} \]

Alternative 13: 44.3% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-231}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-172} \lor \neg \left(b \leq 1.2 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -3.3e+109)
     (/ (* b (- x)) (* y a))
     (if (<= b 6e-254)
       t_1
       (if (<= b 2.7e-231)
         (/ (- b) (* y (/ a x)))
         (if (or (<= b 5e-172) (not (<= b 1.2e-9)))
           t_1
           (/ x (* a (+ y (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -3.3e+109) {
		tmp = (b * -x) / (y * a);
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 2.7e-231) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 5e-172) || !(b <= 1.2e-9)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-3.3d+109)) then
        tmp = (b * -x) / (y * a)
    else if (b <= 6d-254) then
        tmp = t_1
    else if (b <= 2.7d-231) then
        tmp = -b / (y * (a / x))
    else if ((b <= 5d-172) .or. (.not. (b <= 1.2d-9))) then
        tmp = t_1
    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 t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -3.3e+109) {
		tmp = (b * -x) / (y * a);
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 2.7e-231) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 5e-172) || !(b <= 1.2e-9)) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -3.3e+109:
		tmp = (b * -x) / (y * a)
	elif b <= 6e-254:
		tmp = t_1
	elif b <= 2.7e-231:
		tmp = -b / (y * (a / x))
	elif (b <= 5e-172) or not (b <= 1.2e-9):
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -3.3e+109)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(y * a));
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 2.7e-231)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif ((b <= 5e-172) || !(b <= 1.2e-9))
		tmp = t_1;
	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)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -3.3e+109)
		tmp = (b * -x) / (y * a);
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 2.7e-231)
		tmp = -b / (y * (a / x));
	elseif ((b <= 5e-172) || ~((b <= 1.2e-9)))
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+109], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-254], t$95$1, If[LessEqual[b, 2.7e-231], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 5e-172], N[Not[LessEqual[b, 1.2e-9]], $MachinePrecision]], t$95$1, N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.2999999999999999e109

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

      1. associate-/l* 97.2%

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

      2. div-exp 68.6%

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

      3. exp-to-pow 68.6%

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

      4. sub-neg 68.6%

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

      5. metadata-eval 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in t around 0 94.4%

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

   6. Taylor expanded in b around 0 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

      5. times-frac 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in b around inf 53.0%

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

   if -3.2999999999999999e109 < b < 6.00000000000000023e-254 or 2.70000000000000023e-231 < b < 4.9999999999999999e-172 or 1.2e-9 < b

   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. Taylor expanded in y around 0 79.9%

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

      1. associate-/l* 81.3%

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

      2. div-exp 72.6%

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

      3. exp-to-pow 72.8%

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

      4. sub-neg 72.8%

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

      5. metadata-eval 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in t around 0 53.6%

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

   6. Taylor expanded in b around 0 41.4%

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

      1. +-commutative 41.4%

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

      2. associate-*r* 41.4%

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

      3. distribute-rgt-out 42.5%

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

      4. unpow2 42.5%

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

   8. Simplified 42.5%

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

   9. Taylor expanded in b around inf 50.7%

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

       1. associate-*r* 50.7%

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

       2. *-commutative 50.7%

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

       3. unpow2 50.7%

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

   11. Simplified 50.7%

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

   if 6.00000000000000023e-254 < b < 2.70000000000000023e-231

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 4.9999999999999999e-172 < b < 1.2e-9

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 65.3%

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

      1. associate-/l* 70.9%

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

      2. div-exp 70.8%

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

      3. exp-to-pow 71.6%

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

      4. sub-neg 71.6%

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

      5. metadata-eval 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in t around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-231}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-172} \lor \neg \left(b \leq 1.2 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 45.1% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-230}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 10^{-172} \lor \neg \left(b \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -1e+110)
     (/ (- (/ x a) (/ (* x b) a)) y)
     (if (<= b 6e-254)
       t_1
       (if (<= b 4e-230)
         (/ (- b) (* y (/ a x)))
         (if (or (<= b 1e-172) (not (<= b 1.3e-9)))
           t_1
           (/ x (* a (+ y (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -1e+110) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 4e-230) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 1e-172) || !(b <= 1.3e-9)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-1d+110)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 6d-254) then
        tmp = t_1
    else if (b <= 4d-230) then
        tmp = -b / (y * (a / x))
    else if ((b <= 1d-172) .or. (.not. (b <= 1.3d-9))) then
        tmp = t_1
    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 t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -1e+110) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 6e-254) {
		tmp = t_1;
	} else if (b <= 4e-230) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 1e-172) || !(b <= 1.3e-9)) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -1e+110:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 6e-254:
		tmp = t_1
	elif b <= 4e-230:
		tmp = -b / (y * (a / x))
	elif (b <= 1e-172) or not (b <= 1.3e-9):
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -1e+110)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 4e-230)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif ((b <= 1e-172) || !(b <= 1.3e-9))
		tmp = t_1;
	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)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -1e+110)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 6e-254)
		tmp = t_1;
	elseif (b <= 4e-230)
		tmp = -b / (y * (a / x));
	elseif ((b <= 1e-172) || ~((b <= 1.3e-9)))
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+110], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6e-254], t$95$1, If[LessEqual[b, 4e-230], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1e-172], N[Not[LessEqual[b, 1.3e-9]], $MachinePrecision]], t$95$1, N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1e110

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

      1. associate-/l* 97.2%

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

      2. div-exp 68.6%

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

      3. exp-to-pow 68.6%

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

      4. sub-neg 68.6%

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

      5. metadata-eval 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in t around 0 94.4%

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

   6. Taylor expanded in b around 0 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

      5. times-frac 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in y around 0 55.8%

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

   if -1e110 < b < 6.00000000000000023e-254 or 4.00000000000000019e-230 < b < 1e-172 or 1.3000000000000001e-9 < b

   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. Taylor expanded in y around 0 79.9%

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

      1. associate-/l* 81.3%

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

      2. div-exp 72.6%

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

      3. exp-to-pow 72.8%

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

      4. sub-neg 72.8%

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

      5. metadata-eval 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in t around 0 53.6%

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

   6. Taylor expanded in b around 0 41.4%

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

      1. +-commutative 41.4%

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

      2. associate-*r* 41.4%

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

      3. distribute-rgt-out 42.5%

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

      4. unpow2 42.5%

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

   8. Simplified 42.5%

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

   9. Taylor expanded in b around inf 50.7%

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

       1. associate-*r* 50.7%

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

       2. *-commutative 50.7%

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

       3. unpow2 50.7%

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

   11. Simplified 50.7%

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

   if 6.00000000000000023e-254 < b < 4.00000000000000019e-230

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 1e-172 < b < 1.3000000000000001e-9

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 65.3%

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

      1. associate-/l* 70.9%

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

      2. div-exp 70.8%

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

      3. exp-to-pow 71.6%

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

      4. sub-neg 71.6%

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

      5. metadata-eval 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in t around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-230}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 10^{-172} \lor \neg \left(b \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 15: 45.3% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-172} \lor \neg \left(b \leq 3.9 \cdot 10^{-10}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -4.3e+80)
     (/ (- (/ x y) (/ (* x b) y)) a)
     (if (<= b 5.6e-254)
       t_1
       (if (<= b 6.2e-232)
         (/ (- b) (* y (/ a x)))
         (if (or (<= b 6.5e-172) (not (<= b 3.9e-10)))
           t_1
           (/ x (* a (+ y (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -4.3e+80) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 5.6e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 6.5e-172) || !(b <= 3.9e-10)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-4.3d+80)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else if (b <= 5.6d-254) then
        tmp = t_1
    else if (b <= 6.2d-232) then
        tmp = -b / (y * (a / x))
    else if ((b <= 6.5d-172) .or. (.not. (b <= 3.9d-10))) then
        tmp = t_1
    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 t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -4.3e+80) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 5.6e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 6.5e-172) || !(b <= 3.9e-10)) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -4.3e+80:
		tmp = ((x / y) - ((x * b) / y)) / a
	elif b <= 5.6e-254:
		tmp = t_1
	elif b <= 6.2e-232:
		tmp = -b / (y * (a / x))
	elif (b <= 6.5e-172) or not (b <= 3.9e-10):
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -4.3e+80)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	elseif (b <= 5.6e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif ((b <= 6.5e-172) || !(b <= 3.9e-10))
		tmp = t_1;
	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)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -4.3e+80)
		tmp = ((x / y) - ((x * b) / y)) / a;
	elseif (b <= 5.6e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = -b / (y * (a / x));
	elseif ((b <= 6.5e-172) || ~((b <= 3.9e-10)))
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.3e+80], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 5.6e-254], t$95$1, If[LessEqual[b, 6.2e-232], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 6.5e-172], N[Not[LessEqual[b, 3.9e-10]], $MachinePrecision]], t$95$1, N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.30000000000000004e80

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. associate-/l* 95.2%

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

      2. div-exp 68.4%

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

      3. exp-to-pow 68.4%

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

      4. sub-neg 68.4%

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

      5. metadata-eval 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around 0 90.4%

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

   6. Taylor expanded in b around 0 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

      4. *-commutative 48.1%

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

      5. times-frac 45.6%

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

   8. Simplified 45.6%

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

   9. Taylor expanded in a around 0 55.2%

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

   if -4.30000000000000004e80 < b < 5.59999999999999966e-254 or 6.1999999999999998e-232 < b < 6.50000000000000012e-172 or 3.9e-10 < b

   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. Taylor expanded in y around 0 79.8%

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

      1. associate-/l* 81.2%

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

      2. div-exp 72.8%

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

      3. exp-to-pow 73.0%

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

      4. sub-neg 73.0%

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

      5. metadata-eval 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in t around 0 53.1%

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

   6. Taylor expanded in b around 0 42.2%

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

      1. +-commutative 42.2%

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

      2. associate-*r* 42.2%

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

      3. distribute-rgt-out 42.7%

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

      4. unpow2 42.7%

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

   8. Simplified 42.7%

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

   9. Taylor expanded in b around inf 51.2%

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

       1. associate-*r* 51.2%

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

       2. *-commutative 51.2%

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

       3. unpow2 51.2%

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

   11. Simplified 51.2%

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

   if 5.59999999999999966e-254 < b < 6.1999999999999998e-232

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 6.50000000000000012e-172 < b < 3.9e-10

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 65.3%

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

      1. associate-/l* 70.9%

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

      2. div-exp 70.8%

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

      3. exp-to-pow 71.6%

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

      4. sub-neg 71.6%

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

      5. metadata-eval 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in t around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-172} \lor \neg \left(b \leq 3.9 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 16: 45.7% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{if}\;b \leq -5 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-171} \lor \neg \left(b \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* (* a 0.5) (* y (* b b))))))
   (if (<= b -5e+80)
     (- (/ x (* y a)) (/ (* x (/ b y)) a))
     (if (<= b 5.8e-254)
       t_1
       (if (<= b 6.2e-232)
         (/ (- b) (* y (/ a x)))
         (if (or (<= b 1.9e-171) (not (<= b 1.3e-9)))
           t_1
           (/ x (* a (+ y (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -5e+80) {
		tmp = (x / (y * a)) - ((x * (b / y)) / a);
	} else if (b <= 5.8e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 1.9e-171) || !(b <= 1.3e-9)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((a * 0.5d0) * (y * (b * b)))
    if (b <= (-5d+80)) then
        tmp = (x / (y * a)) - ((x * (b / y)) / a)
    else if (b <= 5.8d-254) then
        tmp = t_1
    else if (b <= 6.2d-232) then
        tmp = -b / (y * (a / x))
    else if ((b <= 1.9d-171) .or. (.not. (b <= 1.3d-9))) then
        tmp = t_1
    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 t_1 = x / ((a * 0.5) * (y * (b * b)));
	double tmp;
	if (b <= -5e+80) {
		tmp = (x / (y * a)) - ((x * (b / y)) / a);
	} else if (b <= 5.8e-254) {
		tmp = t_1;
	} else if (b <= 6.2e-232) {
		tmp = -b / (y * (a / x));
	} else if ((b <= 1.9e-171) || !(b <= 1.3e-9)) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a * 0.5) * (y * (b * b)))
	tmp = 0
	if b <= -5e+80:
		tmp = (x / (y * a)) - ((x * (b / y)) / a)
	elif b <= 5.8e-254:
		tmp = t_1
	elif b <= 6.2e-232:
		tmp = -b / (y * (a / x))
	elif (b <= 1.9e-171) or not (b <= 1.3e-9):
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a * 0.5) * Float64(y * Float64(b * b))))
	tmp = 0.0
	if (b <= -5e+80)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x * Float64(b / y)) / a));
	elseif (b <= 5.8e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	elseif ((b <= 1.9e-171) || !(b <= 1.3e-9))
		tmp = t_1;
	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)
	t_1 = x / ((a * 0.5) * (y * (b * b)));
	tmp = 0.0;
	if (b <= -5e+80)
		tmp = (x / (y * a)) - ((x * (b / y)) / a);
	elseif (b <= 5.8e-254)
		tmp = t_1;
	elseif (b <= 6.2e-232)
		tmp = -b / (y * (a / x));
	elseif ((b <= 1.9e-171) || ~((b <= 1.3e-9)))
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a * 0.5), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+80], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-254], t$95$1, If[LessEqual[b, 6.2e-232], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.9e-171], N[Not[LessEqual[b, 1.3e-9]], $MachinePrecision]], t$95$1, N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.99999999999999961e80

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. associate-/l* 95.2%

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

      2. div-exp 68.4%

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

      3. exp-to-pow 68.4%

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

      4. sub-neg 68.4%

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

      5. metadata-eval 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around 0 90.4%

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

   6. Taylor expanded in b around 0 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

      4. *-commutative 48.1%

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

      5. times-frac 45.6%

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

   8. Simplified 45.6%

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

      1. associate-*l/ 55.3%

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

   10. Applied egg-rr 55.3%

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

   if -4.99999999999999961e80 < b < 5.7999999999999999e-254 or 6.1999999999999998e-232 < b < 1.90000000000000011e-171 or 1.3000000000000001e-9 < b

   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. Taylor expanded in y around 0 79.8%

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

      1. associate-/l* 81.2%

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

      2. div-exp 72.8%

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

      3. exp-to-pow 73.0%

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

      4. sub-neg 73.0%

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

      5. metadata-eval 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in t around 0 53.1%

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

   6. Taylor expanded in b around 0 42.2%

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

      1. +-commutative 42.2%

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

      2. associate-*r* 42.2%

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

      3. distribute-rgt-out 42.7%

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

      4. unpow2 42.7%

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

   8. Simplified 42.7%

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

   9. Taylor expanded in b around inf 51.2%

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

       1. associate-*r* 51.2%

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

       2. *-commutative 51.2%

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

       3. unpow2 51.2%

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

   11. Simplified 51.2%

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

   if 5.7999999999999999e-254 < b < 6.1999999999999998e-232

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-exp 100.0%

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

      3. exp-to-pow 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 62.9%

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

   6. Taylor expanded in b around 0 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

      5. times-frac 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in b around inf 83.9%

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

       1. mul-1-neg 83.9%

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

       2. associate-/l* 83.9%

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

       3. associate-*l/ 83.9%

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

       4. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if 1.90000000000000011e-171 < b < 1.3000000000000001e-9

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 65.3%

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

      1. associate-/l* 70.9%

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

      2. div-exp 70.8%

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

      3. exp-to-pow 71.6%

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

      4. sub-neg 71.6%

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

      5. metadata-eval 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in t around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-171} \lor \neg \left(b \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{\left(a \cdot 0.5\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 17: 42.0% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+113}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-254} \lor \neg \left(b \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.42e+113)
   (/ (* b (- x)) (* y a))
   (if (or (<= b 5.5e-254) (not (<= b 1.3e-9)))
     (/ x (* a (* b (* y (* b 0.5)))))
     (/ x (* a (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.42e+113) {
		tmp = (b * -x) / (y * a);
	} else if ((b <= 5.5e-254) || !(b <= 1.3e-9)) {
		tmp = x / (a * (b * (y * (b * 0.5))));
	} 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 <= (-1.42d+113)) then
        tmp = (b * -x) / (y * a)
    else if ((b <= 5.5d-254) .or. (.not. (b <= 1.3d-9))) then
        tmp = x / (a * (b * (y * (b * 0.5d0))))
    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 <= -1.42e+113) {
		tmp = (b * -x) / (y * a);
	} else if ((b <= 5.5e-254) || !(b <= 1.3e-9)) {
		tmp = x / (a * (b * (y * (b * 0.5))));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.42e+113:
		tmp = (b * -x) / (y * a)
	elif (b <= 5.5e-254) or not (b <= 1.3e-9):
		tmp = x / (a * (b * (y * (b * 0.5))))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.42e+113)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(y * a));
	elseif ((b <= 5.5e-254) || !(b <= 1.3e-9))
		tmp = Float64(x / Float64(a * Float64(b * Float64(y * Float64(b * 0.5)))));
	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 <= -1.42e+113)
		tmp = (b * -x) / (y * a);
	elseif ((b <= 5.5e-254) || ~((b <= 1.3e-9)))
		tmp = x / (a * (b * (y * (b * 0.5))));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.42e+113], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 5.5e-254], N[Not[LessEqual[b, 1.3e-9]], $MachinePrecision]], N[(x / N[(a * N[(b * N[(y * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.42e113

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

      1. associate-/l* 97.2%

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

      2. div-exp 68.6%

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

      3. exp-to-pow 68.6%

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

      4. sub-neg 68.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 68.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 68.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 94.4%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 53.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. +-commutative 53.0%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 53.0%

         \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 53.0%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 53.0%

         \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      5. times-frac 50.0%

         \[\leadsto \frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   8. Simplified 50.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   9. Taylor expanded in b around inf 53.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -1.42e113 < b < 5.4999999999999999e-254 or 1.3000000000000001e-9 < 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. Taylor expanded in y around 0 81.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 83.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 74.1%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 74.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 74.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 74.2%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 55.7%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 42.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + \left(0.5 \cdot \left({b}^{2} \cdot y\right) + b \cdot y\right)\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 42.7%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{\left(b \cdot y + 0.5 \cdot \left({b}^{2} \cdot y\right)\right)}\right)} \]

      2. associate-*r* 42.7%

         \[\leadsto \frac{x}{a \cdot \left(y + \left(b \cdot y + \color{blue}{\left(0.5 \cdot {b}^{2}\right) \cdot y}\right)\right)} \]

      3. distribute-rgt-out 43.8%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot \left(b + 0.5 \cdot {b}^{2}\right)}\right)} \]

      4. unpow2 43.8%

         \[\leadsto \frac{x}{a \cdot \left(y + y \cdot \left(b + 0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right)\right)} \]

   8. Simplified 43.8%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot \left(b + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   9. Taylor expanded in b around inf 49.8%

      \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)}} \]
   10. Step-by-step derivation

       1. *-commutative 49.8%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot \left({b}^{2} \cdot y\right)\right) \cdot 0.5}} \]

       2. associate-*l* 49.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left({b}^{2} \cdot y\right) \cdot 0.5\right)}} \]

       3. *-commutative 49.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(0.5 \cdot \left({b}^{2} \cdot y\right)\right)}} \]

       4. associate-*r* 49.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(0.5 \cdot {b}^{2}\right) \cdot y\right)}} \]

       5. unpow2 49.8%

          \[\leadsto \frac{x}{a \cdot \left(\left(0.5 \cdot \color{blue}{\left(b \cdot b\right)}\right) \cdot y\right)} \]

       6. *-commutative 49.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

       7. associate-*r* 49.8%

          \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(\left(0.5 \cdot b\right) \cdot b\right)}\right)} \]

       8. associate-*r* 44.2%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(y \cdot \left(0.5 \cdot b\right)\right) \cdot b\right)}} \]

       9. *-commutative 44.2%

          \[\leadsto \frac{x}{a \cdot \left(\left(y \cdot \color{blue}{\left(b \cdot 0.5\right)}\right) \cdot b\right)} \]

   11. Simplified 44.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(\left(y \cdot \left(b \cdot 0.5\right)\right) \cdot b\right)}} \]

   if 5.4999999999999999e-254 < b < 1.3000000000000001e-9

   1. Initial program 95.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 66.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 69.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 69.9%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 70.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 70.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 70.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 41.1%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 41.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   8. Simplified 41.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+113}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-254} \lor \neg \left(b \leq 1.3 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(b \cdot \left(y \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 18: 35.6% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6.2e-232) (/ (* b (- x)) (* y a)) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.2e-232) {
		tmp = (b * -x) / (y * a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6.2d-232) then
        tmp = (b * -x) / (y * a)
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.2e-232) {
		tmp = (b * -x) / (y * a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6.2e-232:
		tmp = (b * -x) / (y * a)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6.2e-232)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6.2e-232)
		tmp = (b * -x) / (y * a);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6.2e-232], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.1999999999999998e-232

   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 y around 0 80.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 82.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 73.4%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 73.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 73.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 73.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 73.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 52.4%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 33.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. +-commutative 33.5%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 33.5%

         \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 33.5%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 33.5%

         \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      5. times-frac 32.8%

         \[\leadsto \frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   9. Taylor expanded in b around inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if 6.1999999999999998e-232 < b

   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. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 82.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 71.5%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 71.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 71.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 71.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 71.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 64.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 37.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   8. Simplified 37.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 19: 33.8% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5e-50) (/ (- b) (* y (/ a x))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e-50) {
		tmp = -b / (y * (a / x));
	} 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 (b <= (-1.5d-50)) then
        tmp = -b / (y * (a / x))
    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 (b <= -1.5e-50) {
		tmp = -b / (y * (a / x));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.5e-50:
		tmp = -b / (y * (a / x))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.5e-50)
		tmp = Float64(Float64(-b) / Float64(y * Float64(a / x)));
	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 (b <= -1.5e-50)
		tmp = -b / (y * (a / x));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5e-50], N[((-b) / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.49999999999999995e-50

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 86.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 86.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 67.5%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 67.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 67.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 67.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 73.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 36.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 36.6%

         \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 36.6%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 36.6%

         \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      5. times-frac 35.1%

         \[\leadsto \frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   8. Simplified 35.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   9. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. mul-1-neg 37.9%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 36.7%

          \[\leadsto -\color{blue}{\frac{b}{\frac{a \cdot y}{x}}} \]

       3. associate-*l/ 36.6%

          \[\leadsto -\frac{b}{\color{blue}{\frac{a}{x} \cdot y}} \]

       4. *-commutative 36.6%

          \[\leadsto -\frac{b}{\color{blue}{y \cdot \frac{a}{x}}} \]

   11. Simplified 36.6%

       \[\leadsto \color{blue}{-\frac{b}{y \cdot \frac{a}{x}}} \]

   if -1.49999999999999995e-50 < b

   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 y around 0 78.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 81.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 74.3%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 74.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 74.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 74.6%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 74.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 52.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 29.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{-b}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 20: 31.5% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6.2e-232) (/ (* b (- x)) (* y a)) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.2e-232) {
		tmp = (b * -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 (b <= 6.2d-232) then
        tmp = (b * -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 (b <= 6.2e-232) {
		tmp = (b * -x) / (y * a);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6.2e-232:
		tmp = (b * -x) / (y * a)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6.2e-232)
		tmp = Float64(Float64(b * Float64(-x)) / Float64(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 (b <= 6.2e-232)
		tmp = (b * -x) / (y * a);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6.2e-232], N[(N[(b * (-x)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.1999999999999998e-232

   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 y around 0 80.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 82.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 73.4%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 73.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 73.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 73.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 73.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 52.4%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 33.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. +-commutative 33.5%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 33.5%

         \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 33.5%

         \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 33.5%

         \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      5. times-frac 32.8%

         \[\leadsto \frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   9. Taylor expanded in b around inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if 6.1999999999999998e-232 < b

   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. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   3. Step-by-step derivation

      1. associate-/l* 82.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

      2. div-exp 71.5%

         \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

      3. exp-to-pow 71.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

      4. sub-neg 71.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

      5. metadata-eval 71.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

   4. Simplified 71.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

   5. Taylor expanded in t around 0 64.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 28.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{b \cdot \left(-x\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 21: 31.7% 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. Taylor expanded in y around 0 81.0%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
3. Step-by-step derivation

   1. associate-/l* 82.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\log a \cdot \left(t - 1\right) - b}}}} \]

   2. div-exp 72.5%

      \[\leadsto \frac{x}{\frac{y}{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}} \]

   3. exp-to-pow 72.7%

      \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}} \]

   4. sub-neg 72.7%

      \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}} \]

   5. metadata-eval 72.7%

      \[\leadsto \frac{x}{\frac{y}{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}} \]

4. Simplified 72.7%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}} \]

5. Taylor expanded in t around 0 58.2%

   \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

6. Taylor expanded in b around 0 28.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

7. Final simplification 28.9%

   \[\leadsto \frac{x}{y \cdot a} \]

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 2023279 
(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))