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

Percentage Accurate: 98.5% → 98.5%

Time: 31.1s

Alternatives: 24

Speedup: 1.0×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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)) + (log(a) * (t + (-1.0d0)))) - 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)) + (Math.log(a) * (t + -1.0))) - b))) / y;
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Final simplification 98.9%

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

Alternative 2: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+108} \lor \neg \left(y \leq 2050000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.7e+108) (not (<= y 2050000.0)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.7e+108) || !(y <= 2050000.0)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.7d+108)) .or. (.not. (y <= 2050000.0d0))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.7e+108) || !(y <= 2050000.0)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.7e+108) or not (y <= 2050000.0):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.7e+108) || !(y <= 2050000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.7e+108) || ~((y <= 2050000.0)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.7e+108], N[Not[LessEqual[y, 2050000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6999999999999997e108 or 2.05e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.5%

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

      1. +-commutative 94.5%

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

      2. mul-1-neg 94.5%

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

      3. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

   if -8.6999999999999997e108 < y < 2.05e6

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 94.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+108} \lor \neg \left(y \leq 2050000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ t_2 := {a}^{\left(t + -1\right)}\\ t_3 := \frac{t_2}{e^{b}} \cdot \frac{x}{y}\\ t_4 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+123}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{\frac{y}{t_2}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.185:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y))
        (t_2 (pow a (+ t -1.0)))
        (t_3 (* (/ t_2 (exp b)) (/ x y)))
        (t_4 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -9e+123)
     t_4
     (if (<= y -2.3e-60)
       t_3
       (if (<= y -5e-209)
         t_1
         (if (<= y 7e-299)
           (/ x (/ y t_2))
           (if (<= y 2.7e-170) t_1 (if (<= y 0.185) t_3 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double t_2 = pow(a, (t + -1.0));
	double t_3 = (t_2 / exp(b)) * (x / y);
	double t_4 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -9e+123) {
		tmp = t_4;
	} else if (y <= -2.3e-60) {
		tmp = t_3;
	} else if (y <= -5e-209) {
		tmp = t_1;
	} else if (y <= 7e-299) {
		tmp = x / (y / t_2);
	} else if (y <= 2.7e-170) {
		tmp = t_1;
	} else if (y <= 0.185) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = (x / (a * exp(b))) / y
    t_2 = a ** (t + (-1.0d0))
    t_3 = (t_2 / exp(b)) * (x / y)
    t_4 = ((x * (z ** y)) / a) / y
    if (y <= (-9d+123)) then
        tmp = t_4
    else if (y <= (-2.3d-60)) then
        tmp = t_3
    else if (y <= (-5d-209)) then
        tmp = t_1
    else if (y <= 7d-299) then
        tmp = x / (y / t_2)
    else if (y <= 2.7d-170) then
        tmp = t_1
    else if (y <= 0.185d0) then
        tmp = t_3
    else
        tmp = t_4
    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 * Math.exp(b))) / y;
	double t_2 = Math.pow(a, (t + -1.0));
	double t_3 = (t_2 / Math.exp(b)) * (x / y);
	double t_4 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -9e+123) {
		tmp = t_4;
	} else if (y <= -2.3e-60) {
		tmp = t_3;
	} else if (y <= -5e-209) {
		tmp = t_1;
	} else if (y <= 7e-299) {
		tmp = x / (y / t_2);
	} else if (y <= 2.7e-170) {
		tmp = t_1;
	} else if (y <= 0.185) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	t_2 = math.pow(a, (t + -1.0))
	t_3 = (t_2 / math.exp(b)) * (x / y)
	t_4 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -9e+123:
		tmp = t_4
	elif y <= -2.3e-60:
		tmp = t_3
	elif y <= -5e-209:
		tmp = t_1
	elif y <= 7e-299:
		tmp = x / (y / t_2)
	elif y <= 2.7e-170:
		tmp = t_1
	elif y <= 0.185:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	t_2 = a ^ Float64(t + -1.0)
	t_3 = Float64(Float64(t_2 / exp(b)) * Float64(x / y))
	t_4 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -9e+123)
		tmp = t_4;
	elseif (y <= -2.3e-60)
		tmp = t_3;
	elseif (y <= -5e-209)
		tmp = t_1;
	elseif (y <= 7e-299)
		tmp = Float64(x / Float64(y / t_2));
	elseif (y <= 2.7e-170)
		tmp = t_1;
	elseif (y <= 0.185)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * exp(b))) / y;
	t_2 = a ^ (t + -1.0);
	t_3 = (t_2 / exp(b)) * (x / y);
	t_4 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -9e+123)
		tmp = t_4;
	elseif (y <= -2.3e-60)
		tmp = t_3;
	elseif (y <= -5e-209)
		tmp = t_1;
	elseif (y <= 7e-299)
		tmp = x / (y / t_2);
	elseif (y <= 2.7e-170)
		tmp = t_1;
	elseif (y <= 0.185)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 / N[Exp[b], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9e+123], t$95$4, If[LessEqual[y, -2.3e-60], t$95$3, If[LessEqual[y, -5e-209], t$95$1, If[LessEqual[y, 7e-299], N[(x / N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-170], t$95$1, If[LessEqual[y, 0.185], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.99999999999999965e123 or 0.185 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 93.4%

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

      1. exp-sum 67.6%

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

      2. *-commutative 67.6%

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

      3. exp-to-pow 67.6%

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

      4. exp-to-pow 67.7%

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

      5. sub-neg 67.7%

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

      6. metadata-eval 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around 0 85.0%

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

   if -8.99999999999999965e123 < y < -2.3000000000000001e-60 or 2.6999999999999999e-170 < y < 0.185

   1. Initial program 99.0%

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

      1. associate-*l/ 96.3%

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

      2. *-commutative 96.3%

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

      3. +-commutative 96.3%

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

      4. associate--l+ 96.3%

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

      5. exp-sum 84.0%

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

      6. *-commutative 84.0%

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

      7. exp-to-pow 84.8%

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

      8. sub-neg 84.8%

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

      9. metadata-eval 84.8%

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

      10. exp-diff 78.0%

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

      11. *-commutative 78.0%

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

      12. exp-to-pow 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in y around 0 82.5%

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

      1. exp-to-pow 83.3%

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

      2. sub-neg 83.3%

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

      3. metadata-eval 83.3%

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

   7. Simplified 83.3%

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

   if -2.3000000000000001e-60 < y < -5.0000000000000005e-209 or 6.99999999999999981e-299 < y < 2.6999999999999999e-170

   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. Add Preprocessing

   3. Taylor expanded in t around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around 0 88.4%

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

      1. exp-neg 88.4%

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

      2. associate-*r/ 88.4%

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

      3. *-rgt-identity 88.4%

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

      4. +-commutative 88.4%

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

      5. exp-sum 88.4%

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

      6. rem-exp-log 90.1%

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

   8. Simplified 90.1%

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

   if -5.0000000000000005e-209 < y < 6.99999999999999981e-299

   1. Initial program 94.3%

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

   3. Taylor expanded in b around 0 78.8%

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

      1. exp-sum 78.8%

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

      2. *-commutative 78.8%

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

      3. exp-to-pow 78.8%

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

      4. exp-to-pow 79.5%

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

      5. sub-neg 79.5%

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

      6. metadata-eval 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in y around 0 78.8%

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

      1. associate-/l* 83.4%

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

      2. exp-to-pow 84.5%

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

      3. sub-neg 84.5%

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

      4. metadata-eval 84.5%

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

      5. +-commutative 84.5%

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

   8. Simplified 84.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 0.185:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{y \cdot e^{b}} \cdot \frac{x}{a}\\ t_2 := \frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow z y) (* y (exp b))) (/ x a)))
        (t_2 (/ x (/ y (pow a (+ t -1.0))))))
   (if (<= t -5.8e+62)
     t_2
     (if (<= t 1.6e-144)
       t_1
       (if (<= t 1.75e-7)
         (/ (/ (* x (pow z y)) a) y)
         (if (<= t 3.4e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(z, y) / (y * exp(b))) * (x / a);
	double t_2 = x / (y / pow(a, (t + -1.0)));
	double tmp;
	if (t <= -5.8e+62) {
		tmp = t_2;
	} else if (t <= 1.6e-144) {
		tmp = t_1;
	} else if (t <= 1.75e-7) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (t <= 3.4e+27) {
		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 = ((z ** y) / (y * exp(b))) * (x / a)
    t_2 = x / (y / (a ** (t + (-1.0d0))))
    if (t <= (-5.8d+62)) then
        tmp = t_2
    else if (t <= 1.6d-144) then
        tmp = t_1
    else if (t <= 1.75d-7) then
        tmp = ((x * (z ** y)) / a) / y
    else if (t <= 3.4d+27) 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 = (Math.pow(z, y) / (y * Math.exp(b))) * (x / a);
	double t_2 = x / (y / Math.pow(a, (t + -1.0)));
	double tmp;
	if (t <= -5.8e+62) {
		tmp = t_2;
	} else if (t <= 1.6e-144) {
		tmp = t_1;
	} else if (t <= 1.75e-7) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (t <= 3.4e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(z, y) / (y * math.exp(b))) * (x / a)
	t_2 = x / (y / math.pow(a, (t + -1.0)))
	tmp = 0
	if t <= -5.8e+62:
		tmp = t_2
	elif t <= 1.6e-144:
		tmp = t_1
	elif t <= 1.75e-7:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif t <= 3.4e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((z ^ y) / Float64(y * exp(b))) * Float64(x / a))
	t_2 = Float64(x / Float64(y / (a ^ Float64(t + -1.0))))
	tmp = 0.0
	if (t <= -5.8e+62)
		tmp = t_2;
	elseif (t <= 1.6e-144)
		tmp = t_1;
	elseif (t <= 1.75e-7)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (t <= 3.4e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z ^ y) / (y * exp(b))) * (x / a);
	t_2 = x / (y / (a ^ (t + -1.0)));
	tmp = 0.0;
	if (t <= -5.8e+62)
		tmp = t_2;
	elseif (t <= 1.6e-144)
		tmp = t_1;
	elseif (t <= 1.75e-7)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (t <= 3.4e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+62], t$95$2, If[LessEqual[t, 1.6e-144], t$95$1, If[LessEqual[t, 1.75e-7], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 3.4e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.79999999999999968e62 or 3.4e27 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 85.8%

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

      1. exp-sum 62.3%

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

      2. *-commutative 62.3%

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

      3. exp-to-pow 62.3%

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

      4. exp-to-pow 62.3%

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

      5. sub-neg 62.3%

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

      6. metadata-eval 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around 0 77.8%

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

      1. associate-/l* 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

      5. +-commutative 77.8%

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

   8. Simplified 77.8%

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

   if -5.79999999999999968e62 < t < 1.59999999999999986e-144 or 1.74999999999999992e-7 < t < 3.4e27

   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. Step-by-step derivation

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

      3. +-commutative 91.9%

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

      4. associate--l+ 91.9%

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

      5. exp-sum 85.6%

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

      6. *-commutative 85.6%

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

      7. exp-to-pow 86.4%

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

      8. sub-neg 86.4%

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

      9. metadata-eval 86.4%

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

      10. exp-diff 79.2%

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

      11. *-commutative 79.2%

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

      12. exp-to-pow 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in t around 0 80.7%

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

      1. times-frac 81.5%

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

   7. Simplified 81.5%

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

   if 1.59999999999999986e-144 < t < 1.74999999999999992e-7

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0 86.4%

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

      1. exp-sum 86.5%

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

      2. *-commutative 86.5%

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

      3. exp-to-pow 86.5%

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

      4. exp-to-pow 88.6%

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

      5. sub-neg 88.6%

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

      6. metadata-eval 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in t around 0 88.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{{z}^{y}}{y \cdot e^{b}} \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{{z}^{y}}{y \cdot e^{b}} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{a}^{\left(t + -1\right)}}{e^{b}}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-60}:\\ \;\;\;\;t_1 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 0.165:\\ \;\;\;\;\frac{x \cdot t_1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow a (+ t -1.0)) (exp b))) (t_2 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -9e+123)
     t_2
     (if (<= y -4.3e-60)
       (* t_1 (/ x y))
       (if (<= y -1.4e-204)
         (/ (/ x (* a (exp b))) y)
         (if (<= y 0.165) (/ (* x t_1) 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)) / exp(b);
	double t_2 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -9e+123) {
		tmp = t_2;
	} else if (y <= -4.3e-60) {
		tmp = t_1 * (x / y);
	} else if (y <= -1.4e-204) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 0.165) {
		tmp = (x * t_1) / 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))) / exp(b)
    t_2 = ((x * (z ** y)) / a) / y
    if (y <= (-9d+123)) then
        tmp = t_2
    else if (y <= (-4.3d-60)) then
        tmp = t_1 * (x / y)
    else if (y <= (-1.4d-204)) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 0.165d0) then
        tmp = (x * t_1) / 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)) / Math.exp(b);
	double t_2 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -9e+123) {
		tmp = t_2;
	} else if (y <= -4.3e-60) {
		tmp = t_1 * (x / y);
	} else if (y <= -1.4e-204) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 0.165) {
		tmp = (x * t_1) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t + -1.0)) / math.exp(b)
	t_2 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -9e+123:
		tmp = t_2
	elif y <= -4.3e-60:
		tmp = t_1 * (x / y)
	elif y <= -1.4e-204:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 0.165:
		tmp = (x * t_1) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((a ^ Float64(t + -1.0)) / exp(b))
	t_2 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -9e+123)
		tmp = t_2;
	elseif (y <= -4.3e-60)
		tmp = Float64(t_1 * Float64(x / y));
	elseif (y <= -1.4e-204)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 0.165)
		tmp = Float64(Float64(x * t_1) / 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)) / exp(b);
	t_2 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -9e+123)
		tmp = t_2;
	elseif (y <= -4.3e-60)
		tmp = t_1 * (x / y);
	elseif (y <= -1.4e-204)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 0.165)
		tmp = (x * t_1) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9e+123], t$95$2, If[LessEqual[y, -4.3e-60], N[(t$95$1 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-204], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 0.165], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.99999999999999965e123 or 0.165000000000000008 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 93.4%

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

      1. exp-sum 67.6%

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

      2. *-commutative 67.6%

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

      3. exp-to-pow 67.6%

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

      4. exp-to-pow 67.7%

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

      5. sub-neg 67.7%

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

      6. metadata-eval 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around 0 85.0%

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

   if -8.99999999999999965e123 < y < -4.3000000000000001e-60

   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/ 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. exp-sum 84.2%

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

      6. *-commutative 84.2%

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

      7. exp-to-pow 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 71.1%

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

      11. *-commutative 71.1%

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

      12. exp-to-pow 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 82.1%

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

      1. exp-to-pow 82.1%

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

      2. sub-neg 82.1%

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

      3. metadata-eval 82.1%

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

   7. Simplified 82.1%

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

   if -4.3000000000000001e-60 < y < -1.4e-204

   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. Add Preprocessing

   3. Taylor expanded in t around 0 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in y around 0 88.8%

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

      1. exp-neg 88.8%

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

      2. associate-*r/ 88.8%

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

      3. *-rgt-identity 88.8%

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

      4. +-commutative 88.8%

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

      5. exp-sum 88.8%

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

      6. rem-exp-log 90.7%

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

   8. Simplified 90.7%

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

   if -1.4e-204 < y < 0.165000000000000008

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 97.0%

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

      1. div-exp 86.0%

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

      2. exp-to-pow 87.3%

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

      3. sub-neg 87.3%

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

      4. metadata-eval 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 0.165:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+126} \lor \neg \left(y \leq 0.185\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6e+126) (not (<= y 0.185)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+126) || !(y <= 0.185)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.6d+126)) .or. (.not. (y <= 0.185d0))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+126) || !(y <= 0.185)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.6e+126) or not (y <= 0.185):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.6e+126) || !(y <= 0.185))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.6e+126) || ~((y <= 0.185)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.6e+126], N[Not[LessEqual[y, 0.185]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000018e126 or 0.185 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 94.2%

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

      1. exp-sum 68.2%

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

      2. *-commutative 68.2%

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

      3. exp-to-pow 68.3%

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

      4. exp-to-pow 68.3%

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

      5. sub-neg 68.3%

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

      6. metadata-eval 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 85.8%

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

   if -5.60000000000000018e126 < y < 0.185

   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. Add Preprocessing

   3. Taylor expanded in y around 0 94.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+126} \lor \neg \left(y \leq 0.185\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+62} \lor \neg \left(t \leq 3.3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.3e+62) (not (<= t 3.3e+27)))
   (/ x (/ y (pow a (+ t -1.0))))
   (/ x (/ a (/ (pow z y) (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.3e+62) || !(t <= 3.3e+27)) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else {
		tmp = x / (a / (pow(z, y) / (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 <= (-3.3d+62)) .or. (.not. (t <= 3.3d+27))) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else
        tmp = x / (a / ((z ** y) / (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 <= -3.3e+62) || !(t <= 3.3e+27)) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else {
		tmp = x / (a / (Math.pow(z, y) / (y * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.3e+62) or not (t <= 3.3e+27):
		tmp = x / (y / math.pow(a, (t + -1.0)))
	else:
		tmp = x / (a / (math.pow(z, y) / (y * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.3e+62) || !(t <= 3.3e+27))
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	else
		tmp = Float64(x / Float64(a / Float64((z ^ y) / Float64(y * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.3e+62) || ~((t <= 3.3e+27)))
		tmp = x / (y / (a ^ (t + -1.0)));
	else
		tmp = x / (a / ((z ^ y) / (y * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.3e+62], N[Not[LessEqual[t, 3.3e+27]], $MachinePrecision]], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3e62 or 3.2999999999999998e27 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 85.8%

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

      1. exp-sum 62.3%

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

      2. *-commutative 62.3%

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

      3. exp-to-pow 62.3%

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

      4. exp-to-pow 62.3%

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

      5. sub-neg 62.3%

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

      6. metadata-eval 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around 0 77.8%

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

      1. associate-/l* 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

      5. +-commutative 77.8%

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

   8. Simplified 77.8%

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

   if -3.3e62 < t < 3.2999999999999998e27

   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. Step-by-step derivation

      1. associate-/l* 96.9%

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

      2. associate--l+ 96.9%

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

      3. exp-sum 83.8%

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

      4. associate-/r* 83.8%

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

      5. *-commutative 83.8%

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

      6. exp-to-pow 83.8%

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

      7. exp-diff 81.7%

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

      8. *-commutative 81.7%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+62} \lor \neg \left(t \leq 3.3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow a (+ t -1.0))))))
   (if (<= t -1.9e+76)
     t_1
     (if (<= t -7.5e-256)
       (/ (/ x (* a (exp b))) y)
       (if (<= t 1.4e-7) (* (/ x a) (/ (pow z y) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(a, (t + -1.0)));
	double tmp;
	if (t <= -1.9e+76) {
		tmp = t_1;
	} else if (t <= -7.5e-256) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 1.4e-7) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y / (a ** (t + (-1.0d0))))
    if (t <= (-1.9d+76)) then
        tmp = t_1
    else if (t <= (-7.5d-256)) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 1.4d-7) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / Math.pow(a, (t + -1.0)));
	double tmp;
	if (t <= -1.9e+76) {
		tmp = t_1;
	} else if (t <= -7.5e-256) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 1.4e-7) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(a, (t + -1.0)))
	tmp = 0
	if t <= -1.9e+76:
		tmp = t_1
	elif t <= -7.5e-256:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 1.4e-7:
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (a ^ Float64(t + -1.0))))
	tmp = 0.0
	if (t <= -1.9e+76)
		tmp = t_1;
	elseif (t <= -7.5e-256)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 1.4e-7)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (a ^ (t + -1.0)));
	tmp = 0.0;
	if (t <= -1.9e+76)
		tmp = t_1;
	elseif (t <= -7.5e-256)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 1.4e-7)
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+76], t$95$1, If[LessEqual[t, -7.5e-256], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.4e-7], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.90000000000000012e76 or 1.4000000000000001e-7 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 87.2%

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

      1. exp-sum 63.9%

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

      2. *-commutative 63.9%

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

      3. exp-to-pow 63.9%

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

      4. exp-to-pow 63.9%

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

      5. sub-neg 63.9%

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

      6. metadata-eval 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in y around 0 76.1%

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

      1. associate-/l* 76.1%

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

      2. exp-to-pow 76.2%

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

      3. sub-neg 76.2%

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

      4. metadata-eval 76.2%

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

      5. +-commutative 76.2%

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

   8. Simplified 76.2%

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

   if -1.90000000000000012e76 < t < -7.50000000000000005e-256

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. unsub-neg 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in y around 0 78.5%

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

      1. exp-neg 78.5%

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

      2. associate-*r/ 78.5%

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

      3. *-rgt-identity 78.5%

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

      4. +-commutative 78.5%

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

      5. exp-sum 78.5%

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

      6. rem-exp-log 79.4%

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

   8. Simplified 79.4%

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

   if -7.50000000000000005e-256 < t < 1.4000000000000001e-7

   1. Initial program 97.3%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

      3. +-commutative 93.6%

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

      4. associate--l+ 93.6%

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

      5. exp-sum 93.7%

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

      6. *-commutative 93.7%

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

      7. exp-to-pow 95.0%

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

      8. sub-neg 95.0%

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

      9. metadata-eval 95.0%

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

      10. exp-diff 87.7%

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

      11. *-commutative 87.7%

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

      12. exp-to-pow 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t around 0 81.9%

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

      1. times-frac 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in b around 0 77.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.5e+76)
   (/ x (/ y (pow a (+ t -1.0))))
   (if (<= t -8.5e-256)
     (/ (/ x (* a (exp b))) y)
     (if (<= t 1.4e-7)
       (* (/ x a) (/ (pow z y) y))
       (/ (/ (* x (pow a t)) a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+76) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else if (t <= -8.5e-256) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 1.4e-7) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = ((x * pow(a, t)) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.5d+76)) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else if (t <= (-8.5d-256)) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 1.4d-7) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = ((x * (a ** t)) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+76) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else if (t <= -8.5e-256) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 1.4e-7) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.5e+76:
		tmp = x / (y / math.pow(a, (t + -1.0)))
	elif t <= -8.5e-256:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 1.4e-7:
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = ((x * math.pow(a, t)) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.5e+76)
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	elseif (t <= -8.5e-256)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 1.4e-7)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.5e+76)
		tmp = x / (y / (a ^ (t + -1.0)));
	elseif (t <= -8.5e-256)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 1.4e-7)
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = ((x * (a ^ t)) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.5e+76], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-256], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.4e-7], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4999999999999999e76

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 90.8%

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

      1. exp-sum 62.9%

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

      2. *-commutative 62.9%

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

      3. exp-to-pow 62.9%

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

      4. exp-to-pow 62.9%

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

      5. sub-neg 62.9%

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

      6. metadata-eval 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around 0 81.7%

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

      1. associate-/l* 81.7%

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

      2. exp-to-pow 81.7%

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

      3. sub-neg 81.7%

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

      4. metadata-eval 81.7%

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

      5. +-commutative 81.7%

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

   8. Simplified 81.7%

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

   if -1.4999999999999999e76 < t < -8.49999999999999959e-256

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. unsub-neg 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in y around 0 78.5%

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

      1. exp-neg 78.5%

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

      2. associate-*r/ 78.5%

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

      3. *-rgt-identity 78.5%

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

      4. +-commutative 78.5%

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

      5. exp-sum 78.5%

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

      6. rem-exp-log 79.4%

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

   8. Simplified 79.4%

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

   if -8.49999999999999959e-256 < t < 1.4000000000000001e-7

   1. Initial program 97.3%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

      3. +-commutative 93.6%

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

      4. associate--l+ 93.6%

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

      5. exp-sum 93.7%

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

      6. *-commutative 93.7%

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

      7. exp-to-pow 95.0%

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

      8. sub-neg 95.0%

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

      9. metadata-eval 95.0%

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

      10. exp-diff 87.7%

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

      11. *-commutative 87.7%

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

      12. exp-to-pow 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t around 0 81.9%

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

      1. times-frac 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in b around 0 77.5%

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

   if 1.4000000000000001e-7 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 85.0%

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

      1. exp-sum 64.4%

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

      2. *-commutative 64.4%

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

      3. exp-to-pow 64.4%

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

      4. exp-to-pow 64.5%

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

      5. sub-neg 64.5%

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

      6. metadata-eval 64.5%

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

   5. Simplified 64.5%

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

      1. unpow-prod-up 64.6%

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

      2. unpow-1 64.6%

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

   7. Applied egg-rr 64.6%

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

      1. associate-*r/ 64.6%

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

      2. *-rgt-identity 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in y around 0 73.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.9e+85)
   (/ x (/ y (pow a (+ t -1.0))))
   (if (<= t -4.5e-256)
     (/ (/ x (* a (exp b))) y)
     (if (<= t 1.05e-6)
       (/ (/ (* x (pow z y)) a) y)
       (/ (/ (* x (pow a t)) a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e+85) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else if (t <= -4.5e-256) {
		tmp = (x / (a * exp(b))) / y;
	} else if (t <= 1.05e-6) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = ((x * pow(a, t)) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.9d+85)) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else if (t <= (-4.5d-256)) then
        tmp = (x / (a * exp(b))) / y
    else if (t <= 1.05d-6) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = ((x * (a ** t)) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e+85) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else if (t <= -4.5e-256) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (t <= 1.05e-6) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.9e+85:
		tmp = x / (y / math.pow(a, (t + -1.0)))
	elif t <= -4.5e-256:
		tmp = (x / (a * math.exp(b))) / y
	elif t <= 1.05e-6:
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = ((x * math.pow(a, t)) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.9e+85)
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	elseif (t <= -4.5e-256)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (t <= 1.05e-6)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.9e+85)
		tmp = x / (y / (a ^ (t + -1.0)));
	elseif (t <= -4.5e-256)
		tmp = (x / (a * exp(b))) / y;
	elseif (t <= 1.05e-6)
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = ((x * (a ^ t)) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.9e+85], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e-256], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.05e-6], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.8999999999999997e85

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 90.8%

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

      1. exp-sum 62.9%

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

      2. *-commutative 62.9%

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

      3. exp-to-pow 62.9%

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

      4. exp-to-pow 62.9%

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

      5. sub-neg 62.9%

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

      6. metadata-eval 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around 0 81.7%

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

      1. associate-/l* 81.7%

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

      2. exp-to-pow 81.7%

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

      3. sub-neg 81.7%

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

      4. metadata-eval 81.7%

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

      5. +-commutative 81.7%

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

   8. Simplified 81.7%

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

   if -4.8999999999999997e85 < t < -4.5000000000000003e-256

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. unsub-neg 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in y around 0 78.5%

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

      1. exp-neg 78.5%

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

      2. associate-*r/ 78.5%

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

      3. *-rgt-identity 78.5%

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

      4. +-commutative 78.5%

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

      5. exp-sum 78.5%

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

      6. rem-exp-log 79.4%

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

   8. Simplified 79.4%

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

   if -4.5000000000000003e-256 < t < 1.0499999999999999e-6

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 81.4%

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

      1. exp-sum 81.4%

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

      2. *-commutative 81.4%

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

      3. exp-to-pow 81.4%

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

      4. exp-to-pow 82.9%

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

      5. sub-neg 82.9%

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

      6. metadata-eval 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in t around 0 82.9%

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

   if 1.0499999999999999e-6 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 84.6%

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

      1. exp-sum 63.4%

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

      2. *-commutative 63.4%

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

      3. exp-to-pow 63.4%

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

      4. exp-to-pow 63.5%

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

      5. sub-neg 63.5%

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

      6. metadata-eval 63.5%

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

   5. Simplified 63.5%

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

      1. unpow-prod-up 63.6%

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

      2. unpow-1 63.6%

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

   7. Applied egg-rr 63.6%

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

      1. associate-*r/ 63.6%

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

      2. *-rgt-identity 63.6%

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

   9. Simplified 63.6%

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

   10. Taylor expanded in y around 0 73.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -40 \lor \neg \left(b \leq 3.4 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -40.0) (not (<= b 3.4e+102)))
   (/ x (* a (* y (exp b))))
   (* (/ x a) (/ (pow z y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -40.0) || !(b <= 3.4e+102)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x / a) * (pow(z, y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-40.0d0)) .or. (.not. (b <= 3.4d+102))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x / a) * ((z ** y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -40.0) || !(b <= 3.4e+102)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x / a) * (Math.pow(z, y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -40.0) or not (b <= 3.4e+102):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x / a) * (math.pow(z, y) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -40.0) || !(b <= 3.4e+102))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -40.0) || ~((b <= 3.4e+102)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x / a) * ((z ^ y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -40.0], N[Not[LessEqual[b, 3.4e+102]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -40 or 3.4e102 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

      3. +-commutative 91.8%

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

      4. associate--l+ 91.8%

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

      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 72.2%

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

      8. sub-neg 72.2%

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

      9. metadata-eval 72.2%

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

      10. exp-diff 52.6%

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

      11. *-commutative 52.6%

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

      12. exp-to-pow 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in t around 0 70.2%

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

      1. times-frac 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in y around 0 86.8%

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

   if -40 < b < 3.4e102

   1. Initial program 98.2%

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

      1. associate-*l/ 90.1%

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

      2. *-commutative 90.1%

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

      3. +-commutative 90.1%

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

      4. associate--l+ 90.1%

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

      5. exp-sum 73.8%

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

      6. *-commutative 73.8%

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

      7. exp-to-pow 74.7%

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

      8. sub-neg 74.7%

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

      9. metadata-eval 74.7%

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

      10. exp-diff 73.5%

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

      11. *-commutative 73.5%

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

      12. exp-to-pow 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around 0 65.2%

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

      1. times-frac 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in b around 0 67.6%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -40 \lor \neg \left(b \leq 3.4 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-5} \lor \neg \left(b \leq -1.06 \cdot 10^{-232}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e-5) (not (<= b -1.06e-232)))
   (/ x (* a (* y (exp b))))
   (/ (* a (- (* y (/ x y)) (* x b))) (* a (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-5) || !(b <= -1.06e-232)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (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-5)) .or. (.not. (b <= (-1.06d-232)))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (a * ((y * (x / y)) - (x * b))) / (a * (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-5) || !(b <= -1.06e-232)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.5e-5) or not (b <= -1.06e-232):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e-5) || !(b <= -1.06e-232))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(a * Float64(Float64(y * Float64(x / y)) - Float64(x * b))) / Float64(a * 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-5) || ~((b <= -1.06e-232)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e-5], N[Not[LessEqual[b, -1.06e-232]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.50000000000000004e-5 or -1.05999999999999994e-232 < 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. Step-by-step derivation

      1. associate-*l/ 90.2%

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

      2. *-commutative 90.2%

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

      3. +-commutative 90.2%

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

      4. associate--l+ 90.2%

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

      5. exp-sum 73.4%

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

      6. *-commutative 73.4%

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

      7. exp-to-pow 74.0%

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

      8. sub-neg 74.0%

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

      9. metadata-eval 74.0%

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

      10. exp-diff 63.3%

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

      11. *-commutative 63.3%

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

      12. exp-to-pow 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in t around 0 68.7%

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

      1. times-frac 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in y around 0 65.5%

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

   if -1.50000000000000004e-5 < b < -1.05999999999999994e-232

   1. Initial program 99.1%

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

      1. associate-*l/ 92.4%

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

      2. *-commutative 92.4%

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

      3. +-commutative 92.4%

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

      4. associate--l+ 92.4%

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

      5. exp-sum 72.4%

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

      6. *-commutative 72.4%

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

      7. exp-to-pow 73.1%

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

      8. sub-neg 73.1%

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

      9. metadata-eval 73.1%

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

      10. exp-diff 73.1%

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

      11. *-commutative 73.1%

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

      12. exp-to-pow 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in t around 0 61.7%

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

      1. times-frac 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in y around 0 32.9%

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

   9. Taylor expanded in b around 0 32.9%

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

       1. +-commutative 32.9%

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

       2. associate-/r* 34.4%

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

       3. un-div-inv 34.4%

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

       4. associate-*l/ 37.6%

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

       5. associate-*r/ 37.6%

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

       6. frac-add 38.4%

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

       7. div-inv 38.4%

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

       8. *-commutative 38.4%

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

       9. neg-mul-1 38.4%

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

       10. *-commutative 38.4%

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

       11. distribute-rgt-neg-in 38.4%

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

       12. *-commutative 38.4%

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

   11. Applied egg-rr 38.4%

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

       1. +-commutative 38.4%

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

       2. *-commutative 38.4%

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

       3. associate-*r* 48.5%

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

       4. distribute-rgt-out 48.5%

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

       5. *-commutative 48.5%

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

   13. Simplified 48.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-5} \lor \neg \left(b \leq -1.06 \cdot 10^{-232}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in t around 0 81.9%

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

   1. +-commutative 81.9%

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

   2. mul-1-neg 81.9%

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

   3. unsub-neg 81.9%

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

5. Simplified 81.9%

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

6. Taylor expanded in y around 0 58.7%

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

   1. exp-neg 58.7%

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

   2. associate-*r/ 58.7%

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

   3. *-rgt-identity 58.7%

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

   4. +-commutative 58.7%

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

   5. exp-sum 58.7%

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

   6. rem-exp-log 59.3%

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

8. Simplified 59.3%

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

9. Final simplification 59.3%

   \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]
10. Add Preprocessing

Alternative 14: 59.9% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. associate-*l/ 90.7%

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

   2. *-commutative 90.7%

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

   3. +-commutative 90.7%

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

   4. associate--l+ 90.7%

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

   5. exp-sum 73.2%

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

   6. *-commutative 73.2%

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

   7. exp-to-pow 73.8%

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

   8. sub-neg 73.8%

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

   9. metadata-eval 73.8%

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

   10. exp-diff 65.6%

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

   11. *-commutative 65.6%

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

   12. exp-to-pow 65.6%

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

3. Simplified 65.6%

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

5. Taylor expanded in t around 0 67.1%

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

   1. times-frac 66.2%

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

7. Simplified 66.2%

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

8. Taylor expanded in y around 0 57.9%

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

   1. *-un-lft-identity 57.9%

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

   2. times-frac 59.7%

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

10. Applied egg-rr 59.7%

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

    1. associate-*l/ 59.7%

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

    2. *-lft-identity 59.7%

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

12. Simplified 59.7%

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

13. Final simplification 59.7%

    \[\leadsto \frac{\frac{x}{y \cdot e^{b}}}{a} \]
14. Add Preprocessing

Alternative 15: 41.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (- b) y) a))))
   (if (<= b -1.55e+69)
     t_1
     (if (<= b -8e-218)
       (/ (/ x y) a)
       (if (<= b -1.45e-232)
         t_1
         (if (<= b 1.7e+37) (/ (/ x a) y) (/ x (* a (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((-b / y) / a);
	double tmp;
	if (b <= -1.55e+69) {
		tmp = t_1;
	} else if (b <= -8e-218) {
		tmp = (x / y) / a;
	} else if (b <= -1.45e-232) {
		tmp = t_1;
	} else if (b <= 1.7e+37) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((-b / y) / a)
    if (b <= (-1.55d+69)) then
        tmp = t_1
    else if (b <= (-8d-218)) then
        tmp = (x / y) / a
    else if (b <= (-1.45d-232)) then
        tmp = t_1
    else if (b <= 1.7d+37) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((-b / y) / a);
	double tmp;
	if (b <= -1.55e+69) {
		tmp = t_1;
	} else if (b <= -8e-218) {
		tmp = (x / y) / a;
	} else if (b <= -1.45e-232) {
		tmp = t_1;
	} else if (b <= 1.7e+37) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((-b / y) / a)
	tmp = 0
	if b <= -1.55e+69:
		tmp = t_1
	elif b <= -8e-218:
		tmp = (x / y) / a
	elif b <= -1.45e-232:
		tmp = t_1
	elif b <= 1.7e+37:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(Float64(-b) / y) / a))
	tmp = 0.0
	if (b <= -1.55e+69)
		tmp = t_1;
	elseif (b <= -8e-218)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= -1.45e-232)
		tmp = t_1;
	elseif (b <= 1.7e+37)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((-b / y) / a);
	tmp = 0.0;
	if (b <= -1.55e+69)
		tmp = t_1;
	elseif (b <= -8e-218)
		tmp = (x / y) / a;
	elseif (b <= -1.45e-232)
		tmp = t_1;
	elseif (b <= 1.7e+37)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[((-b) / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+69], t$95$1, If[LessEqual[b, -8e-218], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -1.45e-232], t$95$1, If[LessEqual[b, 1.7e+37], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5499999999999999e69 or -8.0000000000000003e-218 < b < -1.45e-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. Step-by-step derivation

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. +-commutative 91.2%

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

      4. associate--l+ 91.2%

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

      5. exp-sum 64.9%

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

      6. *-commutative 64.9%

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

      7. exp-to-pow 64.9%

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

      8. sub-neg 64.9%

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

      9. metadata-eval 64.9%

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

      10. exp-diff 52.6%

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

      11. *-commutative 52.6%

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

      12. exp-to-pow 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in t around 0 68.6%

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

      1. times-frac 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in y around 0 76.2%

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

   9. Taylor expanded in b around 0 42.8%

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

   10. Taylor expanded in b around inf 47.7%

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

       1. mul-1-neg 47.7%

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

       2. *-commutative 47.7%

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

       3. *-commutative 47.7%

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

       4. associate-*r/ 47.6%

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

       5. *-commutative 47.6%

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

       6. distribute-rgt-neg-in 47.6%

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

       7. *-commutative 47.6%

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

       8. associate-/r* 51.1%

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

       9. distribute-neg-frac 51.1%

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

   12. Simplified 51.1%

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

   if -1.5499999999999999e69 < b < -8.0000000000000003e-218

   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. Step-by-step derivation

      1. associate-*l/ 90.4%

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

      2. *-commutative 90.4%

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

      3. +-commutative 90.4%

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

      4. associate--l+ 90.4%

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

      5. exp-sum 75.7%

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

      6. *-commutative 75.7%

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

      7. exp-to-pow 76.2%

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

      8. sub-neg 76.2%

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

      9. metadata-eval 76.2%

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

      10. exp-diff 71.8%

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

      11. *-commutative 71.8%

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

      12. exp-to-pow 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in t around 0 63.2%

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

      1. times-frac 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in y around 0 41.9%

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

      1. *-un-lft-identity 41.9%

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

      2. times-frac 50.1%

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

   10. Applied egg-rr 50.1%

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

       1. associate-*l/ 50.1%

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

       2. *-lft-identity 50.1%

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

   12. Simplified 50.1%

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

   13. Taylor expanded in b around 0 43.2%

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

   if -1.45e-232 < b < 1.70000000000000003e37

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 97.3%

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

      1. exp-sum 82.3%

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

      2. *-commutative 82.3%

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

      3. exp-to-pow 82.3%

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

      4. exp-to-pow 83.9%

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

      5. sub-neg 83.9%

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

      6. metadata-eval 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in t around 0 77.7%

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

   7. Taylor expanded in y around 0 44.9%

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

   if 1.70000000000000003e37 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 70.5%

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

      6. *-commutative 70.5%

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

      7. exp-to-pow 70.5%

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

      8. sub-neg 70.5%

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

      9. metadata-eval 70.5%

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

      10. exp-diff 45.5%

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

      11. *-commutative 45.5%

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

      12. exp-to-pow 45.5%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. times-frac 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in y around 0 86.6%

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

   9. Taylor expanded in b around 0 55.9%

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

   10. Taylor expanded in b around inf 55.9%

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

       1. *-commutative 55.9%

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

   12. Simplified 55.9%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e+69)
   (/ (* x (- b)) (* y a))
   (if (<= b -7.8e-218)
     (/ (/ x y) a)
     (if (<= b -2.5e-232)
       (* x (/ (/ (- b) y) a))
       (if (<= b 4e+32) (/ (/ x a) y) (/ x (* a (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -7.8e-218) {
		tmp = (x / y) / a;
	} else if (b <= -2.5e-232) {
		tmp = x * ((-b / y) / a);
	} else if (b <= 4e+32) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.55d+69)) then
        tmp = (x * -b) / (y * a)
    else if (b <= (-7.8d-218)) then
        tmp = (x / y) / a
    else if (b <= (-2.5d-232)) then
        tmp = x * ((-b / y) / a)
    else if (b <= 4d+32) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -7.8e-218) {
		tmp = (x / y) / a;
	} else if (b <= -2.5e-232) {
		tmp = x * ((-b / y) / a);
	} else if (b <= 4e+32) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e+69:
		tmp = (x * -b) / (y * a)
	elif b <= -7.8e-218:
		tmp = (x / y) / a
	elif b <= -2.5e-232:
		tmp = x * ((-b / y) / a)
	elif b <= 4e+32:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.55e+69)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= -7.8e-218)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= -2.5e-232)
		tmp = Float64(x * Float64(Float64(Float64(-b) / y) / a));
	elseif (b <= 4e+32)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.55e+69)
		tmp = (x * -b) / (y * a);
	elseif (b <= -7.8e-218)
		tmp = (x / y) / a;
	elseif (b <= -2.5e-232)
		tmp = x * ((-b / y) / a);
	elseif (b <= 4e+32)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.55e+69], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.8e-218], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.5e-232], N[(x * N[(N[((-b) / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+32], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.5499999999999999e69

   1. Initial program 100.0%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

      3. +-commutative 89.8%

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

      4. associate--l+ 89.8%

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

      5. exp-sum 65.3%

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

      6. *-commutative 65.3%

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

      7. exp-to-pow 65.3%

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

      8. sub-neg 65.3%

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

      9. metadata-eval 65.3%

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

      10. exp-diff 51.0%

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

      11. *-commutative 51.0%

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

      12. exp-to-pow 51.0%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in t around 0 71.5%

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

      1. times-frac 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around 0 85.9%

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

   9. Taylor expanded in b around 0 47.1%

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

   10. Taylor expanded in b around inf 47.1%

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

   if -1.5499999999999999e69 < b < -7.8e-218

   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. Step-by-step derivation

      1. associate-*l/ 90.4%

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

      2. *-commutative 90.4%

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

      3. +-commutative 90.4%

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

      4. associate--l+ 90.4%

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

      5. exp-sum 75.7%

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

      6. *-commutative 75.7%

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

      7. exp-to-pow 76.2%

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

      8. sub-neg 76.2%

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

      9. metadata-eval 76.2%

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

      10. exp-diff 71.8%

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

      11. *-commutative 71.8%

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

      12. exp-to-pow 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in t around 0 63.2%

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

      1. times-frac 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in y around 0 41.9%

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

      1. *-un-lft-identity 41.9%

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

      2. times-frac 50.1%

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

   10. Applied egg-rr 50.1%

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

       1. associate-*l/ 50.1%

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

       2. *-lft-identity 50.1%

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

   12. Simplified 50.1%

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

   13. Taylor expanded in b around 0 43.2%

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

   if -7.8e-218 < b < -2.5e-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. Step-by-step derivation

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. exp-sum 62.5%

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

      6. *-commutative 62.5%

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

      7. exp-to-pow 62.5%

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

      8. sub-neg 62.5%

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

      9. metadata-eval 62.5%

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

      10. exp-diff 62.5%

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

      11. *-commutative 62.5%

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

      12. exp-to-pow 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in t around 0 51.1%

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

      1. times-frac 38.6%

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

   7. Simplified 38.6%

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

   8. Taylor expanded in y around 0 16.6%

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

   9. Taylor expanded in b around 0 16.6%

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

   10. Taylor expanded in b around inf 51.6%

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

       1. mul-1-neg 51.6%

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

       2. *-commutative 51.6%

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

       3. *-commutative 51.6%

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

       4. associate-*r/ 63.3%

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

       5. *-commutative 63.3%

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

       6. distribute-rgt-neg-in 63.3%

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

       7. *-commutative 63.3%

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

       8. associate-/r* 75.4%

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

       9. distribute-neg-frac 75.4%

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

   12. Simplified 75.4%

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

   if -2.5e-232 < b < 4.00000000000000021e32

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 97.3%

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

      1. exp-sum 82.3%

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

      2. *-commutative 82.3%

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

      3. exp-to-pow 82.3%

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

      4. exp-to-pow 83.9%

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

      5. sub-neg 83.9%

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

      6. metadata-eval 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in t around 0 77.7%

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

   7. Taylor expanded in y around 0 44.9%

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

   if 4.00000000000000021e32 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 70.5%

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

      6. *-commutative 70.5%

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

      7. exp-to-pow 70.5%

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

      8. sub-neg 70.5%

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

      9. metadata-eval 70.5%

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

      10. exp-diff 45.5%

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

      11. *-commutative 45.5%

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

      12. exp-to-pow 45.5%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. times-frac 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in y around 0 86.6%

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

   9. Taylor expanded in b around 0 55.9%

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

   10. Taylor expanded in b around inf 55.9%

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

       1. *-commutative 55.9%

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

   12. Simplified 55.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.1% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e-73)
   (/ (- (/ x y) (* x (/ b y))) a)
   (if (<= b -2.2e-232)
     (/ (* a (- (* y (/ x y)) (* x b))) (* a (* y a)))
     (/ 1.0 (* (/ a x) (* y (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e-73) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -2.2e-232) {
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a));
	} else {
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d-73)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= (-2.2d-232)) then
        tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a))
    else
        tmp = 1.0d0 / ((a / x) * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e-73) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -2.2e-232) {
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a));
	} else {
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e-73:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= -2.2e-232:
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a))
	else:
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e-73)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= -2.2e-232)
		tmp = Float64(Float64(a * Float64(Float64(y * Float64(x / y)) - Float64(x * b))) / Float64(a * Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(Float64(a / x) * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e-73)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= -2.2e-232)
		tmp = (a * ((y * (x / y)) - (x * b))) / (a * (y * a));
	else
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e-73], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.2e-232], N[(N[(a * N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(a / x), $MachinePrecision] * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.50000000000000005e-73

   1. Initial program 99.5%

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

      1. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

      3. +-commutative 91.0%

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

      4. associate--l+ 91.0%

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

      5. exp-sum 70.3%

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

      6. *-commutative 70.3%

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

      7. exp-to-pow 70.7%

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

      8. sub-neg 70.7%

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

      9. metadata-eval 70.7%

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

      10. exp-diff 58.5%

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

      11. *-commutative 58.5%

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

      12. exp-to-pow 58.5%

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

   3. Simplified 58.5%

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

   5. Taylor expanded in t around 0 69.0%

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

      1. times-frac 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in y around 0 70.6%

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

      1. *-un-lft-identity 70.6%

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

      2. times-frac 74.1%

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

   10. Applied egg-rr 74.1%

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

       1. associate-*l/ 74.1%

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

       2. *-lft-identity 74.1%

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

   12. Simplified 74.1%

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

   13. Taylor expanded in b around 0 46.4%

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

       1. +-commutative 46.4%

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

       2. mul-1-neg 46.4%

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

       3. unsub-neg 46.4%

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

       4. *-commutative 46.4%

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

       5. associate-*r/ 45.3%

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

   15. Simplified 45.3%

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

   if -9.50000000000000005e-73 < b < -2.20000000000000002e-232

   1. Initial program 99.6%

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

      1. associate-*l/ 90.3%

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

      2. *-commutative 90.3%

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

      3. +-commutative 90.3%

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

      4. associate--l+ 90.3%

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

      5. exp-sum 71.8%

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

      6. *-commutative 71.8%

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

      7. exp-to-pow 71.9%

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

      8. sub-neg 71.9%

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

      9. metadata-eval 71.9%

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

      10. exp-diff 71.9%

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

      11. *-commutative 71.9%

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

      12. exp-to-pow 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in t around 0 59.4%

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

      1. times-frac 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in y around 0 32.6%

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

   9. Taylor expanded in b around 0 32.6%

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

       1. +-commutative 32.6%

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

       2. associate-/r* 34.7%

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

       3. un-div-inv 34.7%

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

       4. associate-*l/ 36.9%

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

       5. associate-*r/ 36.9%

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

       6. frac-add 40.6%

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

       7. div-inv 40.6%

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

       8. *-commutative 40.6%

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

       9. neg-mul-1 40.6%

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

       10. *-commutative 40.6%

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

       11. distribute-rgt-neg-in 40.6%

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

       12. *-commutative 40.6%

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

   11. Applied egg-rr 40.6%

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

       1. +-commutative 40.6%

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

       2. *-commutative 40.6%

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

       3. associate-*r* 52.3%

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

       4. distribute-rgt-out 52.3%

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

       5. *-commutative 52.3%

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

   13. Simplified 52.3%

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

   if -2.20000000000000002e-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. Step-by-step derivation

      1. associate-*l/ 90.7%

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

      2. *-commutative 90.7%

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

      3. +-commutative 90.7%

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

      4. associate--l+ 90.7%

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

      5. exp-sum 75.4%

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

      6. *-commutative 75.4%

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

      7. exp-to-pow 76.3%

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

      8. sub-neg 76.3%

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

      9. metadata-eval 76.3%

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

      10. exp-diff 67.9%

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

      11. *-commutative 67.9%

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

      12. exp-to-pow 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around 0 68.4%

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

      1. times-frac 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in y around 0 58.1%

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

   9. Taylor expanded in b around 0 47.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. clear-num 47.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}}} \]

       2. inv-pow 47.9%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}\right)}^{-1}} \]

       3. distribute-lft-out 47.9%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot \left(y + b \cdot y\right)}}{x}\right)}^{-1} \]

       4. associate-/l* 47.8%

          \[\leadsto {\color{blue}{\left(\frac{a}{\frac{x}{y + b \cdot y}}\right)}}^{-1} \]

       5. *-un-lft-identity 47.8%

          \[\leadsto {\left(\frac{a}{\frac{x}{\color{blue}{1 \cdot y} + b \cdot y}}\right)}^{-1} \]

       6. distribute-rgt-out 47.8%

          \[\leadsto {\left(\frac{a}{\frac{x}{\color{blue}{y \cdot \left(1 + b\right)}}}\right)}^{-1} \]

   11. Applied egg-rr 47.8%

       \[\leadsto \color{blue}{{\left(\frac{a}{\frac{x}{y \cdot \left(1 + b\right)}}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 47.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y \cdot \left(1 + b\right)}}}} \]

       2. associate-/r/ 48.6%

          \[\leadsto \frac{1}{\color{blue}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}} \]

       3. +-commutative 48.6%

          \[\leadsto \frac{1}{\frac{a}{x} \cdot \left(y \cdot \color{blue}{\left(b + 1\right)}\right)} \]

   13. Simplified 48.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(b + 1\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{a \cdot \left(y \cdot \frac{x}{y} - x \cdot b\right)}{a \cdot \left(y \cdot a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 40.3% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e+69)
   (/ (* x (- b)) (* y a))
   (if (<= b -1.3e-210)
     (/ (/ x y) a)
     (if (<= b -2.5e-232)
       (* x (/ (/ (- b) y) a))
       (* x (/ 1.0 (* a (* y (+ 1.0 b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -1.3e-210) {
		tmp = (x / y) / a;
	} else if (b <= -2.5e-232) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = x * (1.0 / (a * (y * (1.0 + b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.55d+69)) then
        tmp = (x * -b) / (y * a)
    else if (b <= (-1.3d-210)) then
        tmp = (x / y) / a
    else if (b <= (-2.5d-232)) then
        tmp = x * ((-b / y) / a)
    else
        tmp = x * (1.0d0 / (a * (y * (1.0d0 + b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -1.3e-210) {
		tmp = (x / y) / a;
	} else if (b <= -2.5e-232) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = x * (1.0 / (a * (y * (1.0 + b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e+69:
		tmp = (x * -b) / (y * a)
	elif b <= -1.3e-210:
		tmp = (x / y) / a
	elif b <= -2.5e-232:
		tmp = x * ((-b / y) / a)
	else:
		tmp = x * (1.0 / (a * (y * (1.0 + b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.55e+69)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= -1.3e-210)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= -2.5e-232)
		tmp = Float64(x * Float64(Float64(Float64(-b) / y) / a));
	else
		tmp = Float64(x * Float64(1.0 / Float64(a * Float64(y * Float64(1.0 + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.55e+69)
		tmp = (x * -b) / (y * a);
	elseif (b <= -1.3e-210)
		tmp = (x / y) / a;
	elseif (b <= -2.5e-232)
		tmp = x * ((-b / y) / a);
	else
		tmp = x * (1.0 / (a * (y * (1.0 + b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.55e+69], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e-210], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.5e-232], N[(x * N[(N[((-b) / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5499999999999999e69

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 89.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 89.8%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 89.8%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 65.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 65.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 65.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 65.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 65.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 51.0%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 63.3%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 47.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -1.5499999999999999e69 < b < -1.2999999999999999e-210

   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. Step-by-step derivation

      1. associate-*l/ 90.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.7%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.7%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.2%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.2%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.2%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 71.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 71.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 71.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 64.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 41.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-un-lft-identity 41.9%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      2. times-frac 50.1%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

   10. Applied egg-rr 50.1%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]
   11. Step-by-step derivation

       1. associate-*l/ 50.1%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       2. *-lft-identity 50.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

   12. Simplified 50.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot e^{b}}}{a}} \]

   13. Taylor expanded in b around 0 43.2%

       \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if -1.2999999999999999e-210 < b < -2.5e-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. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 100.0%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 62.5%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 62.5%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 62.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 62.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 62.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 38.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 38.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 16.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 16.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 51.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 51.6%

          \[\leadsto -\frac{b \cdot x}{\color{blue}{y \cdot a}} \]

       3. *-commutative 51.6%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{y \cdot a} \]

       4. associate-*r/ 63.3%

          \[\leadsto -\color{blue}{x \cdot \frac{b}{y \cdot a}} \]

       5. *-commutative 63.3%

          \[\leadsto -x \cdot \frac{b}{\color{blue}{a \cdot y}} \]

       6. distribute-rgt-neg-in 63.3%

          \[\leadsto \color{blue}{x \cdot \left(-\frac{b}{a \cdot y}\right)} \]

       7. *-commutative 63.3%

          \[\leadsto x \cdot \left(-\frac{b}{\color{blue}{y \cdot a}}\right) \]

       8. associate-/r* 75.4%

          \[\leadsto x \cdot \left(-\color{blue}{\frac{\frac{b}{y}}{a}}\right) \]

       9. distribute-neg-frac 75.4%

          \[\leadsto x \cdot \color{blue}{\frac{-\frac{b}{y}}{a}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{x \cdot \frac{-\frac{b}{y}}{a}} \]

   if -2.5e-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. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.7%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.7%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 69.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 58.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. clear-num 47.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}}} \]

       2. associate-/r/ 48.5%

          \[\leadsto \color{blue}{\frac{1}{a \cdot y + a \cdot \left(b \cdot y\right)} \cdot x} \]

       3. distribute-lft-out 48.5%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \cdot x \]

       4. *-un-lft-identity 48.5%

          \[\leadsto \frac{1}{a \cdot \left(\color{blue}{1 \cdot y} + b \cdot y\right)} \cdot x \]

       5. distribute-rgt-out 48.5%

          \[\leadsto \frac{1}{a \cdot \color{blue}{\left(y \cdot \left(1 + b\right)\right)}} \cdot x \]

   11. Applied egg-rr 48.5%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \left(y \cdot \left(1 + b\right)\right)} \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.1% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e+69)
   (/ (* x (- b)) (* y a))
   (if (<= b -8e-218)
     (/ (/ x y) a)
     (if (<= b -2.7e-232)
       (* x (/ (/ (- b) y) a))
       (/ 1.0 (* (/ a x) (* y (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -8e-218) {
		tmp = (x / y) / a;
	} else if (b <= -2.7e-232) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.55d+69)) then
        tmp = (x * -b) / (y * a)
    else if (b <= (-8d-218)) then
        tmp = (x / y) / a
    else if (b <= (-2.7d-232)) then
        tmp = x * ((-b / y) / a)
    else
        tmp = 1.0d0 / ((a / x) * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -8e-218) {
		tmp = (x / y) / a;
	} else if (b <= -2.7e-232) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e+69:
		tmp = (x * -b) / (y * a)
	elif b <= -8e-218:
		tmp = (x / y) / a
	elif b <= -2.7e-232:
		tmp = x * ((-b / y) / a)
	else:
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.55e+69)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= -8e-218)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= -2.7e-232)
		tmp = Float64(x * Float64(Float64(Float64(-b) / y) / a));
	else
		tmp = Float64(1.0 / Float64(Float64(a / x) * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.55e+69)
		tmp = (x * -b) / (y * a);
	elseif (b <= -8e-218)
		tmp = (x / y) / a;
	elseif (b <= -2.7e-232)
		tmp = x * ((-b / y) / a);
	else
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.55e+69], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8e-218], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.7e-232], N[(x * N[(N[((-b) / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(a / x), $MachinePrecision] * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5499999999999999e69

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 89.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 89.8%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 89.8%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 65.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 65.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 65.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 65.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 65.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 51.0%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 63.3%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 47.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -1.5499999999999999e69 < b < -8.0000000000000003e-218

   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. Step-by-step derivation

      1. associate-*l/ 90.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.7%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.7%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.2%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.2%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.2%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 71.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 71.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 71.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 64.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 41.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-un-lft-identity 41.9%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      2. times-frac 50.1%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

   10. Applied egg-rr 50.1%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]
   11. Step-by-step derivation

       1. associate-*l/ 50.1%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       2. *-lft-identity 50.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

   12. Simplified 50.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot e^{b}}}{a}} \]

   13. Taylor expanded in b around 0 43.2%

       \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if -8.0000000000000003e-218 < b < -2.6999999999999999e-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. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 100.0%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 62.5%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 62.5%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 62.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 62.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 62.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 38.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 38.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 16.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 16.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 51.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 51.6%

          \[\leadsto -\frac{b \cdot x}{\color{blue}{y \cdot a}} \]

       3. *-commutative 51.6%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{y \cdot a} \]

       4. associate-*r/ 63.3%

          \[\leadsto -\color{blue}{x \cdot \frac{b}{y \cdot a}} \]

       5. *-commutative 63.3%

          \[\leadsto -x \cdot \frac{b}{\color{blue}{a \cdot y}} \]

       6. distribute-rgt-neg-in 63.3%

          \[\leadsto \color{blue}{x \cdot \left(-\frac{b}{a \cdot y}\right)} \]

       7. *-commutative 63.3%

          \[\leadsto x \cdot \left(-\frac{b}{\color{blue}{y \cdot a}}\right) \]

       8. associate-/r* 75.4%

          \[\leadsto x \cdot \left(-\color{blue}{\frac{\frac{b}{y}}{a}}\right) \]

       9. distribute-neg-frac 75.4%

          \[\leadsto x \cdot \color{blue}{\frac{-\frac{b}{y}}{a}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{x \cdot \frac{-\frac{b}{y}}{a}} \]

   if -2.6999999999999999e-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. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.7%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.7%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 69.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 58.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. clear-num 47.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}}} \]

       2. inv-pow 47.9%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}\right)}^{-1}} \]

       3. distribute-lft-out 47.9%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot \left(y + b \cdot y\right)}}{x}\right)}^{-1} \]

       4. associate-/l* 47.8%

          \[\leadsto {\color{blue}{\left(\frac{a}{\frac{x}{y + b \cdot y}}\right)}}^{-1} \]

       5. *-un-lft-identity 47.8%

          \[\leadsto {\left(\frac{a}{\frac{x}{\color{blue}{1 \cdot y} + b \cdot y}}\right)}^{-1} \]

       6. distribute-rgt-out 47.8%

          \[\leadsto {\left(\frac{a}{\frac{x}{\color{blue}{y \cdot \left(1 + b\right)}}}\right)}^{-1} \]

   11. Applied egg-rr 47.8%

       \[\leadsto \color{blue}{{\left(\frac{a}{\frac{x}{y \cdot \left(1 + b\right)}}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 47.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y \cdot \left(1 + b\right)}}}} \]

       2. associate-/r/ 48.6%

          \[\leadsto \frac{1}{\color{blue}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}} \]

       3. +-commutative 48.6%

          \[\leadsto \frac{1}{\frac{a}{x} \cdot \left(y \cdot \color{blue}{\left(b + 1\right)}\right)} \]

   13. Simplified 48.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(b + 1\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 40.3% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e+69)
   (/ (* x (- b)) (* y a))
   (if (<= b -4.3e-212)
     (/ (/ x y) a)
     (if (<= b -7.8e-233) (* x (/ (/ (- b) 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 <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -4.3e-212) {
		tmp = (x / y) / a;
	} else if (b <= -7.8e-233) {
		tmp = x * ((-b / 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 <= (-1.55d+69)) then
        tmp = (x * -b) / (y * a)
    else if (b <= (-4.3d-212)) then
        tmp = (x / y) / a
    else if (b <= (-7.8d-233)) then
        tmp = x * ((-b / 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 <= -1.55e+69) {
		tmp = (x * -b) / (y * a);
	} else if (b <= -4.3e-212) {
		tmp = (x / y) / a;
	} else if (b <= -7.8e-233) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e+69:
		tmp = (x * -b) / (y * a)
	elif b <= -4.3e-212:
		tmp = (x / y) / a
	elif b <= -7.8e-233:
		tmp = x * ((-b / 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 <= -1.55e+69)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= -4.3e-212)
		tmp = Float64(Float64(x / y) / a);
	elseif (b <= -7.8e-233)
		tmp = Float64(x * Float64(Float64(Float64(-b) / 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 <= -1.55e+69)
		tmp = (x * -b) / (y * a);
	elseif (b <= -4.3e-212)
		tmp = (x / y) / a;
	elseif (b <= -7.8e-233)
		tmp = x * ((-b / 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, -1.55e+69], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.3e-212], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -7.8e-233], N[(x * N[(N[((-b) / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5499999999999999e69

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 89.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 89.8%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 89.8%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 65.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 65.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 65.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 65.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 65.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 51.0%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 51.0%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 63.3%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 63.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 47.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -1.5499999999999999e69 < b < -4.29999999999999974e-212

   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. Step-by-step derivation

      1. associate-*l/ 90.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.7%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.7%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.2%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.2%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.2%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 71.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 71.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 71.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 64.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 41.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-un-lft-identity 41.9%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      2. times-frac 50.1%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

   10. Applied egg-rr 50.1%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]
   11. Step-by-step derivation

       1. associate-*l/ 50.1%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       2. *-lft-identity 50.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

   12. Simplified 50.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot e^{b}}}{a}} \]

   13. Taylor expanded in b around 0 43.2%

       \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if -4.29999999999999974e-212 < b < -7.8000000000000002e-233

   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/ 100.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 100.0%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 62.5%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 62.5%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 62.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 62.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 62.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 38.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 38.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 16.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 16.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 51.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 51.6%

          \[\leadsto -\frac{b \cdot x}{\color{blue}{y \cdot a}} \]

       3. *-commutative 51.6%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{y \cdot a} \]

       4. associate-*r/ 63.3%

          \[\leadsto -\color{blue}{x \cdot \frac{b}{y \cdot a}} \]

       5. *-commutative 63.3%

          \[\leadsto -x \cdot \frac{b}{\color{blue}{a \cdot y}} \]

       6. distribute-rgt-neg-in 63.3%

          \[\leadsto \color{blue}{x \cdot \left(-\frac{b}{a \cdot y}\right)} \]

       7. *-commutative 63.3%

          \[\leadsto x \cdot \left(-\frac{b}{\color{blue}{y \cdot a}}\right) \]

       8. associate-/r* 75.4%

          \[\leadsto x \cdot \left(-\color{blue}{\frac{\frac{b}{y}}{a}}\right) \]

       9. distribute-neg-frac 75.4%

          \[\leadsto x \cdot \color{blue}{\frac{-\frac{b}{y}}{a}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{x \cdot \frac{-\frac{b}{y}}{a}} \]

   if -7.8000000000000002e-233 < 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. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.7%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.7%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 69.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 58.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-212}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.35e-214)
   (/ (- (/ x y) (* x (/ b y))) a)
   (if (<= b -2.4e-232)
     (* x (/ (/ (- b) y) a))
     (/ 1.0 (* (/ a x) (* y (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e-214) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -2.4e-232) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.35d-214)) then
        tmp = ((x / y) - (x * (b / y))) / a
    else if (b <= (-2.4d-232)) then
        tmp = x * ((-b / y) / a)
    else
        tmp = 1.0d0 / ((a / x) * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e-214) {
		tmp = ((x / y) - (x * (b / y))) / a;
	} else if (b <= -2.4e-232) {
		tmp = x * ((-b / y) / a);
	} else {
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.35e-214:
		tmp = ((x / y) - (x * (b / y))) / a
	elif b <= -2.4e-232:
		tmp = x * ((-b / y) / a)
	else:
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.35e-214)
		tmp = Float64(Float64(Float64(x / y) - Float64(x * Float64(b / y))) / a);
	elseif (b <= -2.4e-232)
		tmp = Float64(x * Float64(Float64(Float64(-b) / y) / a));
	else
		tmp = Float64(1.0 / Float64(Float64(a / x) * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.35e-214)
		tmp = ((x / y) - (x * (b / y))) / a;
	elseif (b <= -2.4e-232)
		tmp = x * ((-b / y) / a);
	else
		tmp = 1.0 / ((a / x) * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.35e-214], N[(N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.4e-232], N[(x * N[(N[((-b) / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(a / x), $MachinePrecision] * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.35e-214

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.1%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.1%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 71.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 71.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 71.7%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 71.7%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 71.7%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 63.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 63.1%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 63.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 63.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 60.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-un-lft-identity 60.4%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{a \cdot \left(y \cdot e^{b}\right)} \]

      2. times-frac 65.1%

         \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

   10. Applied egg-rr 65.1%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot e^{b}}} \]
   11. Step-by-step derivation

       1. associate-*l/ 65.1%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{a}} \]

       2. *-lft-identity 65.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{a} \]

   12. Simplified 65.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot e^{b}}}{a}} \]

   13. Taylor expanded in b around 0 45.7%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}}}{a} \]
   14. Step-by-step derivation

       1. +-commutative 45.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}}}{a} \]

       2. mul-1-neg 45.7%

          \[\leadsto \frac{\frac{x}{y} + \color{blue}{\left(-\frac{b \cdot x}{y}\right)}}{a} \]

       3. unsub-neg 45.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} - \frac{b \cdot x}{y}}}{a} \]

       4. *-commutative 45.7%

          \[\leadsto \frac{\frac{x}{y} - \frac{\color{blue}{x \cdot b}}{y}}{a} \]

       5. associate-*r/ 44.9%

          \[\leadsto \frac{\frac{x}{y} - \color{blue}{x \cdot \frac{b}{y}}}{a} \]

   15. Simplified 44.9%

       \[\leadsto \frac{\color{blue}{\frac{x}{y} - x \cdot \frac{b}{y}}}{a} \]

   if -1.35e-214 < b < -2.39999999999999999e-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. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 100.0%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 100.0%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 62.5%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 62.5%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 62.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 62.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 62.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 62.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 38.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 38.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 16.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 16.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 51.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 51.6%

          \[\leadsto -\frac{b \cdot x}{\color{blue}{y \cdot a}} \]

       3. *-commutative 51.6%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{y \cdot a} \]

       4. associate-*r/ 63.3%

          \[\leadsto -\color{blue}{x \cdot \frac{b}{y \cdot a}} \]

       5. *-commutative 63.3%

          \[\leadsto -x \cdot \frac{b}{\color{blue}{a \cdot y}} \]

       6. distribute-rgt-neg-in 63.3%

          \[\leadsto \color{blue}{x \cdot \left(-\frac{b}{a \cdot y}\right)} \]

       7. *-commutative 63.3%

          \[\leadsto x \cdot \left(-\frac{b}{\color{blue}{y \cdot a}}\right) \]

       8. associate-/r* 75.4%

          \[\leadsto x \cdot \left(-\color{blue}{\frac{\frac{b}{y}}{a}}\right) \]

       9. distribute-neg-frac 75.4%

          \[\leadsto x \cdot \color{blue}{\frac{-\frac{b}{y}}{a}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{x \cdot \frac{-\frac{b}{y}}{a}} \]

   if -2.39999999999999999e-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. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 90.7%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.7%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 75.4%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 75.4%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 76.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 76.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 76.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 67.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 69.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 58.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 47.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. clear-num 47.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}}} \]

       2. inv-pow 47.9%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y + a \cdot \left(b \cdot y\right)}{x}\right)}^{-1}} \]

       3. distribute-lft-out 47.9%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot \left(y + b \cdot y\right)}}{x}\right)}^{-1} \]

       4. associate-/l* 47.8%

          \[\leadsto {\color{blue}{\left(\frac{a}{\frac{x}{y + b \cdot y}}\right)}}^{-1} \]

       5. *-un-lft-identity 47.8%

          \[\leadsto {\left(\frac{a}{\frac{x}{\color{blue}{1 \cdot y} + b \cdot y}}\right)}^{-1} \]

       6. distribute-rgt-out 47.8%

          \[\leadsto {\left(\frac{a}{\frac{x}{\color{blue}{y \cdot \left(1 + b\right)}}}\right)}^{-1} \]

   11. Applied egg-rr 47.8%

       \[\leadsto \color{blue}{{\left(\frac{a}{\frac{x}{y \cdot \left(1 + b\right)}}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 47.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y \cdot \left(1 + b\right)}}}} \]

       2. associate-/r/ 48.6%

          \[\leadsto \frac{1}{\color{blue}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}} \]

       3. +-commutative 48.6%

          \[\leadsto \frac{1}{\frac{a}{x} \cdot \left(y \cdot \color{blue}{\left(b + 1\right)}\right)} \]

   13. Simplified 48.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(b + 1\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-214}:\\ \;\;\;\;\frac{\frac{x}{y} - x \cdot \frac{b}{y}}{a}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x} \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 36.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.8e+31) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.8e+31) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.8d+31) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.8e+31) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.8e+31:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.8e+31)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.8e+31)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.8e+31], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.79999999999999965e31

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 87.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   4. Step-by-step derivation

      1. exp-sum 74.0%

         \[\leadsto \frac{x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\log a \cdot \left(t - 1\right)}\right)}}{y} \]

      2. *-commutative 74.0%

         \[\leadsto \frac{x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\log a \cdot \left(t - 1\right)}\right)}{y} \]

      3. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \left(\color{blue}{{z}^{y}} \cdot e^{\log a \cdot \left(t - 1\right)}\right)}{y} \]

      4. exp-to-pow 74.8%

         \[\leadsto \frac{x \cdot \left({z}^{y} \cdot \color{blue}{{a}^{\left(t - 1\right)}}\right)}{y} \]

      5. sub-neg 74.8%

         \[\leadsto \frac{x \cdot \left({z}^{y} \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}\right)}{y} \]

      6. metadata-eval 74.8%

         \[\leadsto \frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t + \color{blue}{-1}\right)}\right)}{y} \]

   5. Simplified 74.8%

      \[\leadsto \frac{\color{blue}{x \cdot \left({z}^{y} \cdot {a}^{\left(t + -1\right)}\right)}}{y} \]

   6. Taylor expanded in t around 0 65.5%

      \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

   7. Taylor expanded in y around 0 36.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 4.79999999999999965e31 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 88.6%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 70.5%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 70.5%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 70.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 70.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 70.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 45.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 45.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 45.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 65.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 63.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 86.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 55.9%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]

   10. Taylor expanded in b around inf 55.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   11. Step-by-step derivation

       1. *-commutative 55.9%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   12. Simplified 55.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.5% 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 98.9%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 90.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. *-commutative 90.7%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. +-commutative 90.7%

      \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

   4. associate--l+ 90.7%

      \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

   5. exp-sum 73.2%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 73.2%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 73.8%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 73.8%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 73.8%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 65.6%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 65.6%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 65.6%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 65.6%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 67.1%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
6. Step-by-step derivation

   1. times-frac 66.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Simplified 66.2%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

8. Taylor expanded in y around 0 57.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 33.1%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 33.1%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Alternative 24: 31.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / 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 / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

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. Add Preprocessing

3. Taylor expanded in b around 0 81.4%

   \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
4. Step-by-step derivation

   1. exp-sum 68.9%

      \[\leadsto \frac{x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot e^{\log a \cdot \left(t - 1\right)}\right)}}{y} \]

   2. *-commutative 68.9%

      \[\leadsto \frac{x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot e^{\log a \cdot \left(t - 1\right)}\right)}{y} \]

   3. exp-to-pow 68.9%

      \[\leadsto \frac{x \cdot \left(\color{blue}{{z}^{y}} \cdot e^{\log a \cdot \left(t - 1\right)}\right)}{y} \]

   4. exp-to-pow 69.6%

      \[\leadsto \frac{x \cdot \left({z}^{y} \cdot \color{blue}{{a}^{\left(t - 1\right)}}\right)}{y} \]

   5. sub-neg 69.6%

      \[\leadsto \frac{x \cdot \left({z}^{y} \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}\right)}{y} \]

   6. metadata-eval 69.6%

      \[\leadsto \frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t + \color{blue}{-1}\right)}\right)}{y} \]

5. Simplified 69.6%

   \[\leadsto \frac{\color{blue}{x \cdot \left({z}^{y} \cdot {a}^{\left(t + -1\right)}\right)}}{y} \]

6. Taylor expanded in t around 0 62.3%

   \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

7. Taylor expanded in y around 0 34.7%

   \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

8. Final simplification 34.7%

   \[\leadsto \frac{\frac{x}{a}}{y} \]
9. Add Preprocessing

Developer target: 71.6% 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 2024018 
(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))