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

Percentage Accurate: 98.4% → 98.4%

Time: 21.8s

Alternatives: 18

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

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 97.8%

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

2. Final simplification 97.8%

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

Alternative 2: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+32} \lor \neg \left(y \leq 0.00019\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.2e+32) (not (<= y 0.00019)))
   (/ (* 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 <= -1.2e+32) || !(y <= 0.00019)) {
		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 <= (-1.2d+32)) .or. (.not. (y <= 0.00019d0))) 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 <= -1.2e+32) || !(y <= 0.00019)) {
		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 <= -1.2e+32) or not (y <= 0.00019):
		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 <= -1.2e+32) || !(y <= 0.00019))
		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 <= -1.2e+32) || ~((y <= 0.00019)))
		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, -1.2e+32], N[Not[LessEqual[y, 0.00019]], $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 < -1.19999999999999996e32 or 1.9000000000000001e-4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 92.3%

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

      1. +-commutative 92.3%

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

      2. mul-1-neg 92.3%

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

      3. log-rec 92.3%

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

      4. log-div 92.3%

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

      5. metadata-eval 92.3%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \left(\color{blue}{0} - \log a\right)\right) - b}}{y} \]

      6. associate-+r- 92.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(\left(y \cdot \log z + 0\right) - \log a\right)} - b}}{y} \]

      7. +-rgt-identity 92.3%

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

   4. Simplified 92.3%

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

   if -1.19999999999999996e32 < y < 1.9000000000000001e-4

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 95.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+32} \lor \neg \left(y \leq 0.00019\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]

Alternative 3: 79.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t + -1\right)}\\ t_2 := \frac{t_1}{e^{b}} \cdot \frac{x}{y}\\ t_3 := \frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{if}\;y \leq -42000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{\frac{y}{t_1}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (+ t -1.0)))
        (t_2 (* (/ t_1 (exp b)) (/ x y)))
        (t_3 (/ (/ (* x (pow z y)) y) a)))
   (if (<= y -42000000000000.0)
     t_3
     (if (<= y -3e-187)
       t_2
       (if (<= y 6.5e-240) (/ x (/ y t_1)) (if (<= y 1.6e+18) t_2 t_3))))))

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 = (t_1 / exp(b)) * (x / y);
	double t_3 = ((x * pow(z, y)) / y) / a;
	double tmp;
	if (y <= -42000000000000.0) {
		tmp = t_3;
	} else if (y <= -3e-187) {
		tmp = t_2;
	} else if (y <= 6.5e-240) {
		tmp = x / (y / t_1);
	} else if (y <= 1.6e+18) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a ** (t + (-1.0d0))
    t_2 = (t_1 / exp(b)) * (x / y)
    t_3 = ((x * (z ** y)) / y) / a
    if (y <= (-42000000000000.0d0)) then
        tmp = t_3
    else if (y <= (-3d-187)) then
        tmp = t_2
    else if (y <= 6.5d-240) then
        tmp = x / (y / t_1)
    else if (y <= 1.6d+18) then
        tmp = t_2
    else
        tmp = t_3
    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 = (t_1 / Math.exp(b)) * (x / y);
	double t_3 = ((x * Math.pow(z, y)) / y) / a;
	double tmp;
	if (y <= -42000000000000.0) {
		tmp = t_3;
	} else if (y <= -3e-187) {
		tmp = t_2;
	} else if (y <= 6.5e-240) {
		tmp = x / (y / t_1);
	} else if (y <= 1.6e+18) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t + -1.0))
	t_2 = (t_1 / math.exp(b)) * (x / y)
	t_3 = ((x * math.pow(z, y)) / y) / a
	tmp = 0
	if y <= -42000000000000.0:
		tmp = t_3
	elif y <= -3e-187:
		tmp = t_2
	elif y <= 6.5e-240:
		tmp = x / (y / t_1)
	elif y <= 1.6e+18:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t + -1.0)
	t_2 = Float64(Float64(t_1 / exp(b)) * Float64(x / y))
	t_3 = Float64(Float64(Float64(x * (z ^ y)) / y) / a)
	tmp = 0.0
	if (y <= -42000000000000.0)
		tmp = t_3;
	elseif (y <= -3e-187)
		tmp = t_2;
	elseif (y <= 6.5e-240)
		tmp = Float64(x / Float64(y / t_1));
	elseif (y <= 1.6e+18)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t + -1.0);
	t_2 = (t_1 / exp(b)) * (x / y);
	t_3 = ((x * (z ^ y)) / y) / a;
	tmp = 0.0;
	if (y <= -42000000000000.0)
		tmp = t_3;
	elseif (y <= -3e-187)
		tmp = t_2;
	elseif (y <= 6.5e-240)
		tmp = x / (y / t_1);
	elseif (y <= 1.6e+18)
		tmp = t_2;
	else
		tmp = t_3;
	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[(t$95$1 / N[Exp[b], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -42000000000000.0], t$95$3, If[LessEqual[y, -3e-187], t$95$2, If[LessEqual[y, 6.5e-240], N[(x / N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+18], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e13 or 1.6e18 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate--l+ 85.0%

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

      4. exp-sum 56.6%

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

      5. exp-diff 50.4%

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

      6. *-commutative 50.4%

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

      7. exp-to-pow 50.4%

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

      8. *-commutative 50.4%

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

      9. exp-to-pow 50.4%

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

      10. sub-neg 50.4%

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

      11. metadata-eval 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in t around 0 65.6%

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

      1. times-frac 69.1%

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

   6. Simplified 69.1%

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

      1. associate-*l/ 75.3%

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

      2. clear-num 75.3%

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

      3. un-div-inv 75.3%

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

   8. Applied egg-rr 75.3%

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

   9. Taylor expanded in b around 0 87.8%

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

   if -4.2e13 < y < -3.00000000000000004e-187 or 6.50000000000000007e-240 < y < 1.6e18

   1. Initial program 98.3%

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

      1. associate-*l/ 97.2%

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

      2. *-commutative 97.2%

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

      3. associate--l+ 97.2%

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

      4. exp-sum 95.1%

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

      5. exp-diff 82.3%

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

      6. *-commutative 82.3%

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

      7. exp-to-pow 82.3%

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

      8. *-commutative 82.3%

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

      9. exp-to-pow 83.9%

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

      10. sub-neg 83.9%

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

      11. metadata-eval 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 83.4%

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

      1. associate-/l* 83.8%

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

      2. *-commutative 83.8%

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

      3. sub-neg 83.8%

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

      4. metadata-eval 83.8%

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

      5. *-commutative 83.8%

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

      6. exp-to-pow 85.2%

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

      7. associate-/l* 85.2%

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

      8. associate-/r/ 86.1%

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

      9. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   if -3.00000000000000004e-187 < y < 6.50000000000000007e-240

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 91.5%

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

   3. Taylor expanded in b around 0 83.6%

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

      1. associate-/l* 90.5%

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

      2. sub-neg 90.5%

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

      3. metadata-eval 90.5%

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

      4. exp-to-pow 91.8%

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

      5. +-commutative 91.8%

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

   5. Simplified 91.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -42000000000000:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-187}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \end{array} \]

Alternative 4: 89.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+43} \lor \neg \left(y \leq 6.6 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+43) (not (<= y 6.6e+130)))
   (/ (/ (* x (pow z y)) y) a)
   (/ (* 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 <= -1.1e+43) || !(y <= 6.6e+130)) {
		tmp = ((x * pow(z, y)) / y) / a;
	} 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 <= (-1.1d+43)) .or. (.not. (y <= 6.6d+130))) then
        tmp = ((x * (z ** y)) / y) / a
    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 <= -1.1e+43) || !(y <= 6.6e+130)) {
		tmp = ((x * Math.pow(z, y)) / y) / a;
	} 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 <= -1.1e+43) or not (y <= 6.6e+130):
		tmp = ((x * math.pow(z, y)) / y) / a
	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 <= -1.1e+43) || !(y <= 6.6e+130))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / y) / a);
	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 <= -1.1e+43) || ~((y <= 6.6e+130)))
		tmp = ((x * (z ^ y)) / y) / a;
	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, -1.1e+43], N[Not[LessEqual[y, 6.6e+130]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $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 < -1.1e43 or 6.6e130 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 81.5%

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

      2. *-commutative 81.5%

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

      3. associate--l+ 81.5%

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

      4. exp-sum 55.4%

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

      5. exp-diff 52.2%

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

      6. *-commutative 52.2%

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

      7. exp-to-pow 52.2%

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

      8. *-commutative 52.2%

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

      9. exp-to-pow 52.2%

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

      10. sub-neg 52.2%

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

      11. metadata-eval 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. times-frac 71.8%

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

   6. Simplified 71.8%

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

      1. associate-*l/ 77.3%

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

      2. clear-num 77.3%

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

      3. un-div-inv 77.3%

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

   8. Applied egg-rr 77.3%

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

   9. Taylor expanded in b around 0 91.4%

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

   if -1.1e43 < y < 6.6e130

   1. Initial program 96.5%

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

   2. Taylor expanded in y around 0 93.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+43} \lor \neg \left(y \leq 6.6 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]

Alternative 5: 78.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+26} \lor \neg \left(t \leq 69000000000000\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e+26) (not (<= t 69000000000000.0)))
   (/ 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 <= -1e+26) || !(t <= 69000000000000.0)) {
		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 <= (-1d+26)) .or. (.not. (t <= 69000000000000.0d0))) 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 <= -1e+26) || !(t <= 69000000000000.0)) {
		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 <= -1e+26) or not (t <= 69000000000000.0):
		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 <= -1e+26) || !(t <= 69000000000000.0))
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	else
		tmp = Float64(Float64(x / 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 <= -1e+26) || ~((t <= 69000000000000.0)))
		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, -1e+26], N[Not[LessEqual[t, 69000000000000.0]], $MachinePrecision]], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000005e26 or 6.9e13 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.1%

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

   3. Taylor expanded in b around 0 83.2%

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

      1. associate-/l* 83.2%

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

      2. sub-neg 83.2%

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

      3. metadata-eval 83.2%

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

      4. exp-to-pow 83.2%

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

      5. +-commutative 83.2%

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

   5. Simplified 83.2%

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

   if -1.00000000000000005e26 < t < 6.9e13

   1. Initial program 96.0%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

      3. associate--l+ 86.9%

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

      4. exp-sum 77.2%

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

      5. exp-diff 75.2%

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

      6. *-commutative 75.2%

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

      7. exp-to-pow 75.2%

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

      8. *-commutative 75.2%

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

      9. exp-to-pow 76.5%

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

      10. sub-neg 76.5%

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

      11. metadata-eval 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in t around 0 82.5%

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

      1. times-frac 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+26} \lor \neg \left(t \leq 69000000000000\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \end{array} \]

Alternative 6: 81.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+14} \lor \neg \left(y \leq 2.8 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+14) (not (<= y 2.8e+17)))
   (/ (/ (* x (pow z y)) y) a)
   (/ (* x (pow a t)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+14) || !(y <= 2.8e+17)) {
		tmp = ((x * pow(z, y)) / y) / a;
	} else {
		tmp = (x * pow(a, t)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.1d+14)) .or. (.not. (y <= 2.8d+17))) then
        tmp = ((x * (z ** y)) / y) / a
    else
        tmp = (x * (a ** t)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+14) || !(y <= 2.8e+17)) {
		tmp = ((x * Math.pow(z, y)) / y) / a;
	} else {
		tmp = (x * Math.pow(a, t)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.1e+14) or not (y <= 2.8e+17):
		tmp = ((x * math.pow(z, y)) / y) / a
	else:
		tmp = (x * math.pow(a, t)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.1e+14) || !(y <= 2.8e+17))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / y) / a);
	else
		tmp = Float64(Float64(x * (a ^ t)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.1e+14) || ~((y <= 2.8e+17)))
		tmp = ((x * (z ^ y)) / y) / a;
	else
		tmp = (x * (a ^ t)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.1e+14], N[Not[LessEqual[y, 2.8e+17]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e14 or 2.8e17 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate--l+ 85.0%

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

      4. exp-sum 56.6%

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

      5. exp-diff 50.4%

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

      6. *-commutative 50.4%

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

      7. exp-to-pow 50.4%

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

      8. *-commutative 50.4%

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

      9. exp-to-pow 50.4%

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

      10. sub-neg 50.4%

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

      11. metadata-eval 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in t around 0 65.6%

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

      1. times-frac 69.1%

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

   6. Simplified 69.1%

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

      1. associate-*l/ 75.3%

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

      2. clear-num 75.3%

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

      3. un-div-inv 75.3%

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

   8. Applied egg-rr 75.3%

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

   9. Taylor expanded in b around 0 87.8%

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

   if -4.1e14 < y < 2.8e17

   1. Initial program 96.0%

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

      1. associate-*l/ 91.6%

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

      2. *-commutative 91.6%

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

      3. associate--l+ 91.6%

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

      4. exp-sum 90.2%

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

      5. exp-diff 79.0%

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

      6. *-commutative 79.0%

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

      7. exp-to-pow 79.0%

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

      8. *-commutative 79.0%

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

      9. exp-to-pow 80.3%

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

      10. sub-neg 80.3%

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

      11. metadata-eval 80.3%

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

   3. Simplified 80.3%

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

      1. metadata-eval 80.3%

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

      2. sub-neg 80.3%

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

      3. pow-sub 80.4%

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

      4. pow1 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in y around 0 86.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+14} \lor \neg \left(y \leq 2.8 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 7: 68.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x a) (/ (pow z y) y))))
   (if (<= y -1.25e+26)
     t_1
     (if (<= y 2.3e-156)
       (/ x (/ y (pow a (+ t -1.0))))
       (if (<= y 3.7e+129) (/ (/ x (* y (exp b))) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) * (pow(z, y) / y);
	double tmp;
	if (y <= -1.25e+26) {
		tmp = t_1;
	} else if (y <= 2.3e-156) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else if (y <= 3.7e+129) {
		tmp = (x / (y * exp(b))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) * ((z ** y) / y)
    if (y <= (-1.25d+26)) then
        tmp = t_1
    else if (y <= 2.3d-156) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else if (y <= 3.7d+129) then
        tmp = (x / (y * exp(b))) / a
    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 / a) * (Math.pow(z, y) / y);
	double tmp;
	if (y <= -1.25e+26) {
		tmp = t_1;
	} else if (y <= 2.3e-156) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else if (y <= 3.7e+129) {
		tmp = (x / (y * Math.exp(b))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) * (math.pow(z, y) / y)
	tmp = 0
	if y <= -1.25e+26:
		tmp = t_1
	elif y <= 2.3e-156:
		tmp = x / (y / math.pow(a, (t + -1.0)))
	elif y <= 3.7e+129:
		tmp = (x / (y * math.exp(b))) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) * Float64((z ^ y) / y))
	tmp = 0.0
	if (y <= -1.25e+26)
		tmp = t_1;
	elseif (y <= 2.3e-156)
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	elseif (y <= 3.7e+129)
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) * ((z ^ y) / y);
	tmp = 0.0;
	if (y <= -1.25e+26)
		tmp = t_1;
	elseif (y <= 2.3e-156)
		tmp = x / (y / (a ^ (t + -1.0)));
	elseif (y <= 3.7e+129)
		tmp = (x / (y * exp(b))) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+26], t$95$1, If[LessEqual[y, 2.3e-156], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+129], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e26 or 3.69999999999999978e129 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 81.7%

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

      2. *-commutative 81.7%

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

      3. associate--l+ 81.7%

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

      4. exp-sum 55.9%

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

      5. exp-diff 51.6%

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

      6. *-commutative 51.6%

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

      7. exp-to-pow 51.6%

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

      8. *-commutative 51.6%

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

      9. exp-to-pow 51.6%

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

      10. sub-neg 51.6%

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

      11. metadata-eval 51.6%

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

   3. Simplified 51.6%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. times-frac 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in b around 0 73.2%

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

      1. times-frac 84.0%

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

      2. *-commutative 84.0%

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

   9. Simplified 84.0%

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

   if -1.25e26 < y < 2.3e-156

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 95.4%

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

   3. Taylor expanded in b around 0 78.1%

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

      1. associate-/l* 81.4%

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

      2. sub-neg 81.4%

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

      3. metadata-eval 81.4%

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

      4. exp-to-pow 82.5%

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

      5. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   if 2.3e-156 < y < 3.69999999999999978e129

   1. Initial program 98.5%

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

      1. associate-*l/ 98.5%

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

      2. *-commutative 98.5%

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

      3. associate--l+ 98.5%

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

      4. exp-sum 80.9%

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

      5. exp-diff 65.2%

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

      6. *-commutative 65.2%

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

      7. exp-to-pow 65.2%

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

      8. *-commutative 65.2%

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

      9. exp-to-pow 66.5%

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

      10. sub-neg 66.5%

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

      11. metadata-eval 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in t around 0 67.1%

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

      1. times-frac 65.2%

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

   6. Simplified 65.2%

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

      1. associate-*l/ 68.7%

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

      2. clear-num 68.7%

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

      3. un-div-inv 68.8%

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

   8. Applied egg-rr 68.8%

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

   9. Taylor expanded in y around 0 74.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \end{array} \]

Alternative 8: 74.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) y) a)))
   (if (<= y -3.6e-8)
     t_1
     (if (<= y 3.7e-156)
       (/ x (/ y (pow a (+ t -1.0))))
       (if (<= y 3.4e+33) (/ (/ x (* y (exp b))) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / y) / a;
	double tmp;
	if (y <= -3.6e-8) {
		tmp = t_1;
	} else if (y <= 3.7e-156) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else if (y <= 3.4e+33) {
		tmp = (x / (y * exp(b))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / y) / a
    if (y <= (-3.6d-8)) then
        tmp = t_1
    else if (y <= 3.7d-156) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else if (y <= 3.4d+33) then
        tmp = (x / (y * exp(b))) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / y) / a;
	double tmp;
	if (y <= -3.6e-8) {
		tmp = t_1;
	} else if (y <= 3.7e-156) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else if (y <= 3.4e+33) {
		tmp = (x / (y * Math.exp(b))) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / y) / a
	tmp = 0
	if y <= -3.6e-8:
		tmp = t_1
	elif y <= 3.7e-156:
		tmp = x / (y / math.pow(a, (t + -1.0)))
	elif y <= 3.4e+33:
		tmp = (x / (y * math.exp(b))) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / y) / a)
	tmp = 0.0
	if (y <= -3.6e-8)
		tmp = t_1;
	elseif (y <= 3.7e-156)
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	elseif (y <= 3.4e+33)
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / y) / a;
	tmp = 0.0;
	if (y <= -3.6e-8)
		tmp = t_1;
	elseif (y <= 3.7e-156)
		tmp = x / (y / (a ^ (t + -1.0)));
	elseif (y <= 3.4e+33)
		tmp = (x / (y * exp(b))) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -3.6e-8], t$95$1, If[LessEqual[y, 3.7e-156], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+33], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999981e-8 or 3.3999999999999999e33 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate--l+ 85.0%

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

      4. exp-sum 57.5%

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

      5. exp-diff 52.2%

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

      6. *-commutative 52.2%

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

      7. exp-to-pow 52.2%

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

      8. *-commutative 52.2%

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

      9. exp-to-pow 52.2%

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

      10. sub-neg 52.2%

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

      11. metadata-eval 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in t around 0 66.5%

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

      1. times-frac 70.0%

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

   6. Simplified 70.0%

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

      1. associate-*l/ 76.2%

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

      2. clear-num 76.2%

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

      3. un-div-inv 76.2%

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

   8. Applied egg-rr 76.2%

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

   9. Taylor expanded in b around 0 87.8%

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

   if -3.59999999999999981e-8 < y < 3.7e-156

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 95.3%

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

   3. Taylor expanded in b around 0 79.4%

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

      1. associate-/l* 82.8%

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

      2. sub-neg 82.8%

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

      3. metadata-eval 82.8%

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

      4. exp-to-pow 83.9%

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

      5. +-commutative 83.9%

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

   5. Simplified 83.9%

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

   if 3.7e-156 < y < 3.3999999999999999e33

   1. Initial program 97.8%

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

      1. associate-*l/ 97.8%

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

      2. *-commutative 97.8%

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

      3. associate--l+ 97.8%

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

      4. exp-sum 90.3%

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

      5. exp-diff 72.8%

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

      6. *-commutative 72.8%

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

      7. exp-to-pow 72.8%

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

      8. *-commutative 72.8%

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

      9. exp-to-pow 74.8%

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

      10. sub-neg 74.8%

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

      11. metadata-eval 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. times-frac 67.9%

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

   6. Simplified 67.9%

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

      1. associate-*l/ 70.4%

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

      2. clear-num 70.4%

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

      3. un-div-inv 70.5%

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

   8. Applied egg-rr 70.5%

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

   9. Taylor expanded in y around 0 78.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{y}}{a}\\ \end{array} \]

Alternative 9: 70.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{-28} \lor \neg \left(b \leq 1.85 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;{z}^{y} \cdot \frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.65e-28) (not (<= b 1.85e+15)))
   (/ x (* a (* y (exp b))))
   (* (pow z y) (/ (/ x y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.65e-28) || !(b <= 1.85e+15)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = pow(z, y) * ((x / y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.65d-28)) .or. (.not. (b <= 1.85d+15))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (z ** y) * ((x / y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.65e-28) || !(b <= 1.85e+15)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = Math.pow(z, y) * ((x / y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.65e-28) or not (b <= 1.85e+15):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = math.pow(z, y) * ((x / y) / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.65e-28) || !(b <= 1.85e+15))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64((z ^ y) * Float64(Float64(x / y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.65e-28) || ~((b <= 1.85e+15)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (z ^ y) * ((x / y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.65e-28], N[Not[LessEqual[b, 1.85e+15]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[z, y], $MachinePrecision] * N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.64999999999999994e-28 or 1.85e15 < 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/ 92.0%

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

      2. *-commutative 92.0%

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

      3. associate--l+ 92.0%

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

      4. exp-sum 73.6%

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

      5. exp-diff 55.2%

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

      6. *-commutative 55.2%

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

      7. exp-to-pow 55.2%

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

      8. *-commutative 55.2%

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

      9. exp-to-pow 55.2%

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

      10. sub-neg 55.2%

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

      11. metadata-eval 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in t around 0 69.8%

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

      1. times-frac 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around 0 78.0%

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

   if -2.64999999999999994e-28 < b < 1.85e15

   1. Initial program 95.6%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. associate--l+ 85.5%

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

      4. exp-sum 77.1%

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

      5. exp-diff 77.1%

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

      6. *-commutative 77.1%

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

      7. exp-to-pow 77.1%

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

      8. *-commutative 77.1%

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

      9. exp-to-pow 78.5%

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

      10. sub-neg 78.5%

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

      11. metadata-eval 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. times-frac 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in b around 0 66.7%

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

      1. associate-/l* 66.7%

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

      2. associate-/r/ 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-/r* 67.5%

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

   9. Simplified 67.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{-28} \lor \neg \left(b \leq 1.85 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;{z}^{y} \cdot \frac{\frac{x}{y}}{a}\\ \end{array} \]

Alternative 10: 69.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+29} \lor \neg \left(y \leq 1.8 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e+29) (not (<= y 1.8e+134)))
   (* (/ x a) (/ (pow z y) y))
   (/ (/ x (* y (exp b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+29) || !(y <= 1.8e+134)) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = (x / (y * exp(b))) / 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 ((y <= (-1.35d+29)) .or. (.not. (y <= 1.8d+134))) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = (x / (y * exp(b))) / 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 ((y <= -1.35e+29) || !(y <= 1.8e+134)) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = (x / (y * Math.exp(b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e+29) or not (y <= 1.8e+134):
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = (x / (y * math.exp(b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e+29) || !(y <= 1.8e+134))
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e+29) || ~((y <= 1.8e+134)))
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = (x / (y * exp(b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e+29], N[Not[LessEqual[y, 1.8e+134]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e29 or 1.79999999999999994e134 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 81.5%

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

      2. *-commutative 81.5%

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

      3. associate--l+ 81.5%

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

      4. exp-sum 55.4%

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

      5. exp-diff 52.2%

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

      6. *-commutative 52.2%

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

      7. exp-to-pow 52.2%

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

      8. *-commutative 52.2%

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

      9. exp-to-pow 52.2%

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

      10. sub-neg 52.2%

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

      11. metadata-eval 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. times-frac 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in b around 0 72.9%

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

      1. times-frac 83.8%

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

      2. *-commutative 83.8%

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

   9. Simplified 83.8%

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

   if -1.35e29 < y < 1.79999999999999994e134

   1. Initial program 96.5%

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

      1. associate-*l/ 92.7%

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

      2. *-commutative 92.7%

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

      3. associate--l+ 92.7%

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

      4. exp-sum 86.6%

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

      5. exp-diff 74.4%

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

      6. *-commutative 74.4%

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

      7. exp-to-pow 74.4%

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

      8. *-commutative 74.4%

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

      9. exp-to-pow 75.5%

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

      10. sub-neg 75.5%

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

      11. metadata-eval 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. times-frac 64.0%

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

   6. Simplified 64.0%

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

      1. associate-*l/ 69.8%

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

      2. clear-num 69.8%

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

      3. un-div-inv 69.8%

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

   8. Applied egg-rr 69.8%

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

   9. Taylor expanded in y around 0 71.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+29} \lor \neg \left(y \leq 1.8 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \]

Alternative 11: 58.9% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. associate-*l/ 88.7%

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

   2. *-commutative 88.7%

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

   3. associate--l+ 88.7%

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

   4. exp-sum 75.4%

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

   5. exp-diff 66.4%

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

   6. *-commutative 66.4%

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

   7. exp-to-pow 66.4%

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

   8. *-commutative 66.4%

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

   9. exp-to-pow 67.1%

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

   10. sub-neg 67.1%

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

   11. metadata-eval 67.1%

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

3. Simplified 67.1%

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

4. Taylor expanded in t around 0 67.4%

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

   1. times-frac 66.8%

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

6. Simplified 66.8%

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

7. Taylor expanded in y around 0 59.8%

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

8. Final simplification 59.8%

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

Alternative 12: 58.6% 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 97.8%

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

   1. associate-*l/ 88.7%

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

   2. *-commutative 88.7%

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

   3. associate--l+ 88.7%

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

   4. exp-sum 75.4%

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

   5. exp-diff 66.4%

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

   6. *-commutative 66.4%

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

   7. exp-to-pow 66.4%

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

   8. *-commutative 66.4%

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

   9. exp-to-pow 67.1%

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

   10. sub-neg 67.1%

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

   11. metadata-eval 67.1%

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

3. Simplified 67.1%

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

4. Taylor expanded in t around 0 67.4%

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

   1. times-frac 66.8%

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

6. Simplified 66.8%

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

   1. associate-*l/ 72.5%

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

   2. clear-num 72.5%

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

   3. un-div-inv 72.5%

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

8. Applied egg-rr 72.5%

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

9. Taylor expanded in y around 0 61.7%

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

10. Final simplification 61.7%

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

Alternative 13: 34.7% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + y \cdot b\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{a \cdot t_1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t_1}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* y b))))
   (if (<= y -2.8e-55)
     (/ x (* a t_1))
     (if (<= y 1.6e-74) (/ (/ x y) a) (/ (/ x t_1) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (y * b);
	double tmp;
	if (y <= -2.8e-55) {
		tmp = x / (a * t_1);
	} else if (y <= 1.6e-74) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / t_1) / 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) :: t_1
    real(8) :: tmp
    t_1 = y + (y * b)
    if (y <= (-2.8d-55)) then
        tmp = x / (a * t_1)
    else if (y <= 1.6d-74) then
        tmp = (x / y) / a
    else
        tmp = (x / t_1) / 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 t_1 = y + (y * b);
	double tmp;
	if (y <= -2.8e-55) {
		tmp = x / (a * t_1);
	} else if (y <= 1.6e-74) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / t_1) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (y * b)
	tmp = 0
	if y <= -2.8e-55:
		tmp = x / (a * t_1)
	elif y <= 1.6e-74:
		tmp = (x / y) / a
	else:
		tmp = (x / t_1) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(y * b))
	tmp = 0.0
	if (y <= -2.8e-55)
		tmp = Float64(x / Float64(a * t_1));
	elseif (y <= 1.6e-74)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / t_1) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (y * b);
	tmp = 0.0;
	if (y <= -2.8e-55)
		tmp = x / (a * t_1);
	elseif (y <= 1.6e-74)
		tmp = (x / y) / a;
	else
		tmp = (x / t_1) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-55], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-74], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t$95$1), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999984e-55

   1. Initial program 99.9%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

      3. associate--l+ 86.2%

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

      4. exp-sum 67.0%

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

      5. exp-diff 60.2%

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

      6. *-commutative 60.2%

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

      7. exp-to-pow 60.2%

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

      8. *-commutative 60.2%

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

      9. exp-to-pow 60.3%

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

      10. sub-neg 60.3%

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

      11. metadata-eval 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in t around 0 67.3%

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

      1. times-frac 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in y around 0 49.1%

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

   8. Taylor expanded in b around 0 38.4%

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

   if -2.79999999999999984e-55 < y < 1.5999999999999999e-74

   1. Initial program 95.4%

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

      1. associate-*l/ 89.9%

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

      2. *-commutative 89.9%

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

      3. associate--l+ 89.9%

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

      4. exp-sum 89.9%

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

      5. exp-diff 79.2%

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

      6. *-commutative 79.2%

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

      7. exp-to-pow 79.2%

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

      8. *-commutative 79.2%

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

      9. exp-to-pow 80.5%

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

      10. sub-neg 80.5%

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

      11. metadata-eval 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around 0 69.4%

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

      1. times-frac 66.3%

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

   6. Simplified 66.3%

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

      1. associate-*l/ 71.0%

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

      2. clear-num 71.0%

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

      3. un-div-inv 71.1%

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

   8. Applied egg-rr 71.1%

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

   9. Taylor expanded in y around 0 71.1%

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

   10. Taylor expanded in b around 0 44.8%

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

   if 1.5999999999999999e-74 < y

   1. Initial program 99.3%

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

      1. associate-*l/ 89.3%

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

      2. *-commutative 89.3%

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

      3. associate--l+ 89.3%

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

      4. exp-sum 60.7%

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

      5. exp-diff 52.2%

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

      6. *-commutative 52.2%

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

      7. exp-to-pow 52.2%

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

      8. *-commutative 52.2%

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

      9. exp-to-pow 52.8%

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

      10. sub-neg 52.8%

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

      11. metadata-eval 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in t around 0 64.5%

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

      1. times-frac 63.0%

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

   6. Simplified 63.0%

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

      1. associate-*l/ 70.1%

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

      2. clear-num 70.1%

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

      3. un-div-inv 70.2%

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

   8. Applied egg-rr 70.2%

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

   9. Taylor expanded in y around 0 61.0%

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

   10. Taylor expanded in b around 0 48.7%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]

Alternative 14: 39.7% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9e-7) (/ (- (/ x y) (/ (* x b) y)) a) (/ (/ x (+ y (* y b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9e-7) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = (x / (y + (y * b))) / 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 <= (-9d-7)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else
        tmp = (x / (y + (y * b))) / 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 <= -9e-7) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9e-7:
		tmp = ((x / y) - ((x * b) / y)) / a
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9e-7)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9e-7)
		tmp = ((x / y) - ((x * b) / y)) / a;
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9e-7], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.99999999999999959e-7

   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/ 91.3%

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

      2. *-commutative 91.3%

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

      3. associate--l+ 91.3%

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

      4. exp-sum 69.6%

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

      5. exp-diff 55.1%

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

      6. *-commutative 55.1%

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

      7. exp-to-pow 55.1%

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

      8. *-commutative 55.1%

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

      9. exp-to-pow 55.1%

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

      10. sub-neg 55.1%

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

      11. metadata-eval 55.1%

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

   3. Simplified 55.1%

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

   4. Taylor expanded in t around 0 68.3%

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

      1. times-frac 61.0%

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

   6. Simplified 61.0%

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

      1. associate-*l/ 68.3%

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

      2. clear-num 68.3%

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

      3. un-div-inv 68.3%

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

   8. Applied egg-rr 68.3%

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

   9. Taylor expanded in y around 0 77.2%

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

   10. Taylor expanded in b around 0 48.2%

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

   if -8.99999999999999959e-7 < b

   1. Initial program 96.9%

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

      1. associate-*l/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate--l+ 87.7%

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

      4. exp-sum 77.5%

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

      5. exp-diff 70.6%

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

      6. *-commutative 70.6%

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

      7. exp-to-pow 70.6%

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

      8. *-commutative 70.6%

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

      9. exp-to-pow 71.6%

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

      10. sub-neg 71.6%

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

      11. metadata-eval 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in t around 0 67.1%

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

      1. times-frac 69.0%

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

   6. Simplified 69.0%

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

      1. associate-*l/ 74.0%

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

      2. clear-num 74.0%

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

      3. un-div-inv 74.1%

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

   8. Applied egg-rr 74.1%

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

   9. Taylor expanded in y around 0 56.0%

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

   10. Taylor expanded in b around 0 44.2%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]

Alternative 15: 30.9% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{-178}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.6e-178) (/ (/ x y) a) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.6e-178) {
		tmp = (x / y) / a;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.6d-178) then
        tmp = (x / y) / a
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.6e-178) {
		tmp = (x / y) / a;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.6e-178:
		tmp = (x / y) / a
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.6e-178)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.6e-178)
		tmp = (x / y) / a;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.6e-178], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.6e-178

   1. Initial program 97.1%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

      3. associate--l+ 86.9%

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

      4. exp-sum 73.4%

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

      5. exp-diff 64.1%

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

      6. *-commutative 64.1%

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

      7. exp-to-pow 64.1%

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

      8. *-commutative 64.1%

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

      9. exp-to-pow 64.8%

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

      10. sub-neg 64.8%

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

      11. metadata-eval 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. times-frac 62.5%

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

   6. Simplified 62.5%

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

      1. associate-*l/ 70.9%

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

      2. clear-num 70.9%

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

      3. un-div-inv 70.9%

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

   8. Applied egg-rr 70.9%

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

   9. Taylor expanded in y around 0 62.6%

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

   10. Taylor expanded in b around 0 41.0%

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

   if 1.6e-178 < x

   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/ 92.3%

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

      2. *-commutative 92.3%

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

      3. associate--l+ 92.3%

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

      4. exp-sum 79.3%

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

      5. exp-diff 71.1%

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

      6. *-commutative 71.1%

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

      7. exp-to-pow 71.1%

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

      8. *-commutative 71.1%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in t around 0 70.9%

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

      1. times-frac 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around 0 62.0%

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

   8. Taylor expanded in b around 0 37.1%

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

      1. *-commutative 37.1%

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

   10. Simplified 37.1%

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

       1. div-inv 38.2%

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

       2. *-commutative 38.2%

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

       3. *-commutative 38.2%

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

   12. Applied egg-rr 38.2%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{-178}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]

Alternative 16: 35.3% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 255000000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 255000000.0) (/ (/ x y) a) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 255000000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 255000000.0d0) then
        tmp = (x / y) / a
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 255000000.0) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 255000000.0:
		tmp = (x / y) / a
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 255000000.0)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 255000000.0)
		tmp = (x / y) / a;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 255000000.0], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.55e8

   1. Initial program 97.2%

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

      1. associate-*l/ 87.6%

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

      2. *-commutative 87.6%

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

      3. associate--l+ 87.6%

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

      4. exp-sum 74.7%

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

      5. exp-diff 69.8%

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

      6. *-commutative 69.8%

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

      7. exp-to-pow 69.8%

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

      8. *-commutative 69.8%

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

      9. exp-to-pow 70.7%

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

      10. sub-neg 70.7%

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

      11. metadata-eval 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around 0 66.1%

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

      1. times-frac 66.9%

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

   6. Simplified 66.9%

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

      1. associate-*l/ 72.5%

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

      2. clear-num 72.5%

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

      3. un-div-inv 72.5%

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

   8. Applied egg-rr 72.5%

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

   9. Taylor expanded in y around 0 56.8%

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

   10. Taylor expanded in b around 0 41.3%

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

   if 2.55e8 < 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/ 92.6%

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

      2. *-commutative 92.6%

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

      3. associate--l+ 92.6%

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

      4. exp-sum 77.8%

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

      5. exp-diff 53.7%

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

      6. *-commutative 53.7%

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

      7. exp-to-pow 53.7%

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

      8. *-commutative 53.7%

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

      9. exp-to-pow 53.7%

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

      10. sub-neg 53.7%

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

      11. metadata-eval 53.7%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. times-frac 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in y around 0 79.9%

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

   8. Taylor expanded in b around 0 39.1%

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

   9. Taylor expanded in b around inf 39.1%

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

       1. *-commutative 39.1%

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

   11. Simplified 39.1%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 255000000:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 17: 31.0% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-111}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1e-111) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e-111) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1d-111) then
        tmp = (x / y) / a
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e-111) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1e-111:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1e-111)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1e-111)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1e-111], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000009e-111

   1. Initial program 97.2%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

      3. associate--l+ 87.1%

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

      4. exp-sum 74.4%

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

      5. exp-diff 65.6%

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

      6. *-commutative 65.6%

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

      7. exp-to-pow 65.6%

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

      8. *-commutative 65.6%

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

      9. exp-to-pow 66.4%

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

      10. sub-neg 66.4%

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

      11. metadata-eval 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in t around 0 67.3%

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

      1. times-frac 64.2%

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

   6. Simplified 64.2%

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

      1. associate-*l/ 72.1%

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

      2. clear-num 72.1%

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

      3. un-div-inv 72.2%

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

   8. Applied egg-rr 72.2%

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

   9. Taylor expanded in y around 0 64.4%

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

   10. Taylor expanded in b around 0 40.9%

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

   if 1.00000000000000009e-111 < x

   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/ 92.6%

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

      2. *-commutative 92.6%

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

      3. associate--l+ 92.6%

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

      4. exp-sum 77.7%

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

      5. exp-diff 68.3%

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

      6. *-commutative 68.3%

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

      7. exp-to-pow 68.3%

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

      8. *-commutative 68.3%

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

      9. exp-to-pow 68.9%

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

      10. sub-neg 68.9%

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

      11. metadata-eval 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in t around 0 67.9%

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

      1. times-frac 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in y around 0 57.7%

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

   8. Taylor expanded in b around 0 36.9%

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

      1. *-commutative 36.9%

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

   10. Simplified 36.9%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{-111}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 18: 30.4% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. associate-*l/ 88.7%

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

   2. *-commutative 88.7%

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

   3. associate--l+ 88.7%

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

   4. exp-sum 75.4%

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

   5. exp-diff 66.4%

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

   6. *-commutative 66.4%

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

   7. exp-to-pow 66.4%

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

   8. *-commutative 66.4%

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

   9. exp-to-pow 67.1%

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

   10. sub-neg 67.1%

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

   11. metadata-eval 67.1%

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

3. Simplified 67.1%

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

4. Taylor expanded in t around 0 67.4%

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

   1. times-frac 66.8%

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

6. Simplified 66.8%

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

7. Taylor expanded in y around 0 59.8%

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

8. Taylor expanded in b around 0 36.3%

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

   1. *-commutative 36.3%

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

10. Simplified 36.3%

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

11. Final simplification 36.3%

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

Developer target: 71.5% 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 2023301 
(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))