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

Percentage Accurate: 98.5% → 98.5%

Time: 23.3s

Alternatives: 32

Speedup: 1.0×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

3. Final simplification 99.0%

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

Alternative 2: 87.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+149} \lor \neg \left(y \leq 2 \cdot 10^{+54}\right) \land \left(y \leq 1.25 \cdot 10^{+87} \lor \neg \left(y \leq 2 \cdot 10^{+222}\right)\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.6e+149)
         (and (not (<= y 2e+54)) (or (<= y 1.25e+87) (not (<= y 2e+222)))))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e+149) || (!(y <= 2e+54) && ((y <= 1.25e+87) || !(y <= 2e+222)))) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.6d+149)) .or. (.not. (y <= 2d+54)) .and. (y <= 1.25d+87) .or. (.not. (y <= 2d+222))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.6e+149) || (!(y <= 2e+54) && ((y <= 1.25e+87) || !(y <= 2e+222)))) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.6e+149) or (not (y <= 2e+54) and ((y <= 1.25e+87) or not (y <= 2e+222))):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.6e+149) || (!(y <= 2e+54) && ((y <= 1.25e+87) || !(y <= 2e+222))))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.6e+149) || (~((y <= 2e+54)) && ((y <= 1.25e+87) || ~((y <= 2e+222)))))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.6e+149], And[N[Not[LessEqual[y, 2e+54]], $MachinePrecision], Or[LessEqual[y, 1.25e+87], N[Not[LessEqual[y, 2e+222]], $MachinePrecision]]]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $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 < -2.59999999999999979e149 or 2.0000000000000002e54 < y < 1.24999999999999995e87 or 2.0000000000000001e222 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 58.9%

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

      4. associate-/l* 57.1%

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

      5. *-commutative 57.1%

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

      6. exp-to-pow 57.1%

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

      7. exp-diff 57.1%

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

      8. *-commutative 57.1%

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

      9. exp-to-pow 57.1%

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

      10. sub-neg 57.1%

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

      11. metadata-eval 57.1%

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

   3. Simplified 57.1%

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

   5. Taylor expanded in t around 0 73.3%

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

      1. associate-/r* 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in b around 0 93.0%

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

   if -2.59999999999999979e149 < y < 2.0000000000000002e54 or 1.24999999999999995e87 < y < 2.0000000000000001e222

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 93.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+149} \lor \neg \left(y \leq 2 \cdot 10^{+54}\right) \land \left(y \leq 1.25 \cdot 10^{+87} \lor \neg \left(y \leq 2 \cdot 10^{+222}\right)\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7800000000000 \lor \neg \left(t \leq 6.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7800000000000.0) (not (<= t 6.8e+22)))
   (/ (* x (pow a (+ t -1.0))) y)
   (* x (/ (/ (pow z y) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7800000000000.0) || !(t <= 6.8e+22)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = x * ((pow(z, y) / a) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7800000000000.0d0)) .or. (.not. (t <= 6.8d+22))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = x * (((z ** y) / a) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7800000000000.0) || !(t <= 6.8e+22)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = x * ((Math.pow(z, y) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7800000000000.0) or not (t <= 6.8e+22):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = x * ((math.pow(z, y) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7800000000000.0) || !(t <= 6.8e+22))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7800000000000.0) || ~((t <= 6.8e+22)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = x * (((z ^ y) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7800000000000.0], N[Not[LessEqual[t, 6.8e+22]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.8e12 or 6.8e22 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.8%

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

   4. Taylor expanded in b around 0 85.6%

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

      1. *-commutative 85.6%

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

      2. exp-to-pow 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

      5. +-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -7.8e12 < t < 6.8e22

   1. Initial program 98.1%

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

      1. associate-/l* 97.5%

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

      2. associate--l+ 97.5%

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

      3. exp-sum 85.5%

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

      4. associate-/l* 84.0%

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

      5. *-commutative 84.0%

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

      6. exp-to-pow 84.0%

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

      7. exp-diff 81.7%

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

      8. *-commutative 81.7%

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

      9. exp-to-pow 83.4%

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

      10. sub-neg 83.4%

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

      11. metadata-eval 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. associate-/r* 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7800000000000 \lor \neg \left(t \leq 6.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000 \lor \neg \left(y \leq 1.8 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4000.0) (not (<= y 1.8e+51)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4000.0) || !(y <= 1.8e+51)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4000.0d0)) .or. (.not. (y <= 1.8d+51))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4000.0) || !(y <= 1.8e+51)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4000.0) or not (y <= 1.8e+51):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4000.0) || !(y <= 1.8e+51))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4000.0) || ~((y <= 1.8e+51)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4000.0], N[Not[LessEqual[y, 1.8e+51]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e3 or 1.80000000000000005e51 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 59.6%

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

      4. associate-/l* 57.7%

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

      5. *-commutative 57.7%

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

      6. exp-to-pow 57.7%

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

      7. exp-diff 54.8%

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

      8. *-commutative 54.8%

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

      9. exp-to-pow 54.8%

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

      10. sub-neg 54.8%

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

      11. metadata-eval 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in t around 0 66.5%

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

      1. associate-/r* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in b around 0 80.1%

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

   if -4e3 < y < 1.80000000000000005e51

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 97.1%

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

      1. div-exp 91.2%

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

      2. exp-to-pow 92.5%

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

      3. sub-neg 92.5%

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

      4. metadata-eval 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000 \lor \neg \left(y \leq 1.8 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -17000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-256}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 34000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -17000000000.0)
     t_2
     (if (<= b -4e-18)
       t_1
       (if (<= b 2.9e-256)
         (/ (* x (/ (pow z y) a)) y)
         (if (<= b 34000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double t_2 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -17000000000.0) {
		tmp = t_2;
	} else if (b <= -4e-18) {
		tmp = t_1;
	} else if (b <= 2.9e-256) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (b <= 34000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-17000000000.0d0)) then
        tmp = t_2
    else if (b <= (-4d-18)) then
        tmp = t_1
    else if (b <= 2.9d-256) then
        tmp = (x * ((z ** y) / a)) / y
    else if (b <= 34000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_2 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -17000000000.0) {
		tmp = t_2;
	} else if (b <= -4e-18) {
		tmp = t_1;
	} else if (b <= 2.9e-256) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (b <= 34000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	t_2 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -17000000000.0:
		tmp = t_2
	elif b <= -4e-18:
		tmp = t_1
	elif b <= 2.9e-256:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif b <= 34000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -17000000000.0)
		tmp = t_2;
	elseif (b <= -4e-18)
		tmp = t_1;
	elseif (b <= 2.9e-256)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (b <= 34000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	t_2 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -17000000000.0)
		tmp = t_2;
	elseif (b <= -4e-18)
		tmp = t_1;
	elseif (b <= 2.9e-256)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (b <= 34000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -17000000000.0], t$95$2, If[LessEqual[b, -4e-18], t$95$1, If[LessEqual[b, 2.9e-256], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 34000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7e10 or 3.4e10 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 73.8%

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

      4. associate-/l* 73.8%

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

      5. *-commutative 73.8%

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

      6. exp-to-pow 73.8%

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

      7. exp-diff 62.6%

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

      8. *-commutative 62.6%

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

      9. exp-to-pow 62.6%

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

      10. sub-neg 62.6%

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

      11. metadata-eval 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. associate-/r* 72.0%

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

   7. Simplified 72.0%

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

   8. Taylor expanded in y around 0 89.0%

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

   if -1.7e10 < b < -4.0000000000000003e-18 or 2.89999999999999971e-256 < b < 3.4e10

   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. Add Preprocessing

   3. Taylor expanded in y around 0 80.7%

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

   4. Taylor expanded in b around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. exp-to-pow 81.6%

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

      3. sub-neg 81.6%

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

      4. metadata-eval 81.6%

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

      5. +-commutative 81.6%

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

   6. Simplified 81.6%

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

   if -4.0000000000000003e-18 < b < 2.89999999999999971e-256

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 98.4%

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

      1. exp-sum 81.8%

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

      2. *-commutative 81.8%

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

      3. exp-to-pow 81.8%

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

      4. exp-to-pow 83.2%

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

      5. sub-neg 83.2%

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

      6. metadata-eval 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in t around 0 81.0%

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

      1. associate-*r/ 81.0%

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

   8. Simplified 81.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -17000000000:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-256}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 34000000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+23} \lor \neg \left(b \leq 5700000000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+23) (not (<= b 5700000000.0)))
   (/ x (* a (* y (exp b))))
   (* x (/ (/ (pow z y) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+23) || !(b <= 5700000000.0)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * ((pow(z, y) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.6d+23)) .or. (.not. (b <= 5700000000.0d0))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (((z ** y) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+23) || !(b <= 5700000000.0)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e+23) or not (b <= 5700000000.0):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+23) || !(b <= 5700000000.0))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e+23) || ~((b <= 5700000000.0)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+23], N[Not[LessEqual[b, 5700000000.0]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5999999999999998e23 or 5.7e9 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 74.0%

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

      4. associate-/l* 74.0%

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

      5. *-commutative 74.0%

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

      6. exp-to-pow 74.0%

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

      7. exp-diff 63.5%

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

      8. *-commutative 63.5%

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

      9. exp-to-pow 63.5%

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

      10. sub-neg 63.5%

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

      11. metadata-eval 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in t around 0 72.2%

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

      1. associate-/r* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around 0 89.6%

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

   if -3.5999999999999998e23 < b < 5.7e9

   1. Initial program 98.4%

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

      1. associate-/l* 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 84.0%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. exp-to-pow 82.7%

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

      7. exp-diff 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 83.5%

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

      10. sub-neg 83.5%

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

      11. metadata-eval 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in t around 0 66.6%

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

      1. associate-/r* 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in b around 0 70.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+23} \lor \neg \left(b \leq 5700000000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+25} \lor \neg \left(b \leq 3200000000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.7e+25) (not (<= b 3200000000.0)))
   (/ x (* a (* y (exp b))))
   (/ (* x (/ (pow z y) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+25) || !(b <= 3200000000.0)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x * (pow(z, y) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.7d+25)) .or. (.not. (b <= 3200000000.0d0))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x * ((z ** y) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+25) || !(b <= 3200000000.0)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.7e+25) or not (b <= 3200000000.0):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x * (math.pow(z, y) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.7e+25) || !(b <= 3200000000.0))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.7e+25) || ~((b <= 3200000000.0)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x * ((z ^ y) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.7e+25], N[Not[LessEqual[b, 3200000000.0]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.69999999999999992e25 or 3.2e9 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 74.0%

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

      4. associate-/l* 74.0%

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

      5. *-commutative 74.0%

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

      6. exp-to-pow 74.0%

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

      7. exp-diff 63.5%

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

      8. *-commutative 63.5%

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

      9. exp-to-pow 63.5%

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

      10. sub-neg 63.5%

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

      11. metadata-eval 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in t around 0 72.2%

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

      1. associate-/r* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in y around 0 89.6%

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

   if -1.69999999999999992e25 < b < 3.2e9

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 97.4%

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

      1. exp-sum 84.9%

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

      2. *-commutative 84.9%

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

      3. exp-to-pow 84.9%

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

      4. exp-to-pow 86.4%

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

      5. sub-neg 86.4%

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

      6. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in t around 0 72.1%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+25} \lor \neg \left(b \leq 3200000000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% 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 99.0%

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

   1. associate-/l* 98.7%

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

   2. associate--l+ 98.7%

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

   3. exp-sum 80.0%

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

   4. associate-/l* 79.2%

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

   5. *-commutative 79.2%

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

   6. exp-to-pow 79.2%

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

   7. exp-diff 74.5%

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

   8. *-commutative 74.5%

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

   9. exp-to-pow 75.3%

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

   10. sub-neg 75.3%

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

   11. metadata-eval 75.3%

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

3. Simplified 75.3%

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

5. Taylor expanded in t around 0 68.9%

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

   1. associate-/r* 70.8%

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

7. Simplified 70.8%

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

8. Taylor expanded in y around 0 60.4%

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

9. Final simplification 60.4%

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

Alternative 9: 58.4% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

3. Taylor expanded in y around 0 82.3%

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

   1. div-exp 75.6%

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

   2. exp-to-pow 76.4%

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

   3. sub-neg 76.4%

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

   4. metadata-eval 76.4%

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

5. Simplified 76.4%

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

6. Taylor expanded in t around 0 61.1%

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

7. Final simplification 61.1%

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

Alternative 10: 51.9% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} - \frac{x}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{-232}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.5e-233)
   (/ (- (/ x a) (* b (+ (/ x a) (* b (- (/ (* x b) a) (/ x a)))))) y)
   (if (<= b 3.15e-232)
     (/ x (* a (+ y (* b (* b (+ (* y 0.5) (/ y b)))))))
     (if (<= b 1.65e-174)
       (/ (/ (+ (/ x a) (/ (- (/ x (* a b)) (/ x a)) b)) b) y)
       (/
        (/
         x
         (+ a (* b (+ a (* b (+ (* (* a b) 0.16666666666666666) (* a 0.5)))))))
        y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.5e-233) {
		tmp = ((x / a) - (b * ((x / a) + (b * (((x * b) / a) - (x / a)))))) / y;
	} else if (b <= 3.15e-232) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else if (b <= 1.65e-174) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.5d-233)) then
        tmp = ((x / a) - (b * ((x / a) + (b * (((x * b) / a) - (x / a)))))) / y
    else if (b <= 3.15d-232) then
        tmp = x / (a * (y + (b * (b * ((y * 0.5d0) + (y / b))))))
    else if (b <= 1.65d-174) then
        tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
    else
        tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666d0) + (a * 0.5d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.5e-233) {
		tmp = ((x / a) - (b * ((x / a) + (b * (((x * b) / a) - (x / a)))))) / y;
	} else if (b <= 3.15e-232) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else if (b <= 1.65e-174) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.5e-233:
		tmp = ((x / a) - (b * ((x / a) + (b * (((x * b) / a) - (x / a)))))) / y
	elif b <= 3.15e-232:
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))))
	elif b <= 1.65e-174:
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
	else:
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.5e-233)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x / a) + Float64(b * Float64(Float64(Float64(x * b) / a) - Float64(x / a)))))) / y);
	elseif (b <= 3.15e-232)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(b * Float64(Float64(y * 0.5) + Float64(y / b)))))));
	elseif (b <= 1.65e-174)
		tmp = Float64(Float64(Float64(Float64(x / a) + Float64(Float64(Float64(x / Float64(a * b)) - Float64(x / a)) / b)) / b) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(Float64(a * b) * 0.16666666666666666) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.5e-233)
		tmp = ((x / a) - (b * ((x / a) + (b * (((x * b) / a) - (x / a)))))) / y;
	elseif (b <= 3.15e-232)
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	elseif (b <= 1.65e-174)
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	else
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.5e-233], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.15e-232], N[(x / N[(a * N[(y + N[(b * N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-174], N[(N[(N[(N[(x / a), $MachinePrecision] + N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(N[(a * b), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.5000000000000005e-233

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. div-exp 74.6%

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

      2. exp-to-pow 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 66.4%

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

   7. Taylor expanded in b around 0 24.2%

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

   8. Taylor expanded in b around 0 59.2%

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

   if -8.5000000000000005e-233 < b < 3.15000000000000005e-232

   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%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 81.5%

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

      4. associate-/l* 79.0%

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

      5. *-commutative 79.0%

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

      6. exp-to-pow 79.0%

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

      7. exp-diff 79.0%

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

      8. *-commutative 79.0%

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

      9. exp-to-pow 80.3%

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

      10. sub-neg 80.3%

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

      11. metadata-eval 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in t around 0 73.8%

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

      1. associate-/r* 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in y around 0 40.9%

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

   9. Taylor expanded in b around 0 40.9%

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

   10. Taylor expanded in b around inf 52.4%

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

   if 3.15000000000000005e-232 < b < 1.65e-174

   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. Add Preprocessing

   3. Taylor expanded in y around 0 68.8%

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

      1. div-exp 68.8%

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

      2. exp-to-pow 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around 0 14.4%

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

   7. Taylor expanded in b around 0 14.4%

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

   8. Taylor expanded in b around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. neg-mul-1 57.6%

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

      3. +-commutative 57.6%

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

      4. sub-neg 57.6%

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

      5. distribute-neg-frac2 57.6%

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

   10. Simplified 57.6%

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

   if 1.65e-174 < b

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.4%

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

      1. div-exp 81.7%

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

      2. exp-to-pow 82.7%

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

      3. sub-neg 82.7%

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

      4. metadata-eval 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in t around 0 71.2%

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

   7. Taylor expanded in b around 0 60.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} - \frac{x}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{-232}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + 0.16666666666666666 \cdot \left(y \cdot b\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6.5e-231)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 5.2e-176)
     (/ (/ (+ (/ x a) (/ (- (/ x (* a b)) (/ x a)) b)) b) y)
     (/
      x
      (*
       a
       (+
        y
        (* b (+ y (* b (+ (* y 0.5) (* 0.16666666666666666 (* y b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.5e-231) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 5.2e-176) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (0.16666666666666666 * (y * b))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6.5d-231) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 5.2d-176) then
        tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
    else
        tmp = x / (a * (y + (b * (y + (b * ((y * 0.5d0) + (0.16666666666666666d0 * (y * b))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.5e-231) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 5.2e-176) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (0.16666666666666666 * (y * b))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6.5e-231:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 5.2e-176:
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
	else:
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (0.16666666666666666 * (y * b))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6.5e-231)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 5.2e-176)
		tmp = Float64(Float64(Float64(Float64(x / a) + Float64(Float64(Float64(x / Float64(a * b)) - Float64(x / a)) / b)) / b) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(y * 0.5) + Float64(0.16666666666666666 * Float64(y * b)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6.5e-231)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 5.2e-176)
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	else
		tmp = x / (a * (y + (b * (y + (b * ((y * 0.5) + (0.16666666666666666 * (y * b))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6.5e-231], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.2e-176], N[(N[(N[(N[(x / a), $MachinePrecision] + N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 6.5000000000000004e-231

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. div-exp 72.6%

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

      2. exp-to-pow 73.3%

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

      3. sub-neg 73.3%

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

      4. metadata-eval 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around 0 60.0%

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

   7. Taylor expanded in b around 0 41.6%

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

   8. Taylor expanded in x around 0 52.0%

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

   if 6.5000000000000004e-231 < b < 5.19999999999999984e-176

   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. Add Preprocessing

   3. Taylor expanded in y around 0 68.8%

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

      1. div-exp 68.8%

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

      2. exp-to-pow 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around 0 14.4%

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

   7. Taylor expanded in b around 0 14.4%

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

   8. Taylor expanded in b around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. neg-mul-1 57.6%

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

      3. +-commutative 57.6%

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

      4. sub-neg 57.6%

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

      5. distribute-neg-frac2 57.6%

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

   10. Simplified 57.6%

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

   if 5.19999999999999984e-176 < b

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. associate--l+ 99.0%

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

      3. exp-sum 79.2%

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

      4. associate-/l* 79.2%

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

      5. *-commutative 79.2%

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

      6. exp-to-pow 79.2%

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

      7. exp-diff 75.9%

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

      8. *-commutative 75.9%

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

      9. exp-to-pow 76.9%

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

      10. sub-neg 76.9%

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

      11. metadata-eval 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in t around 0 70.7%

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

      1. associate-/r* 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in y around 0 72.3%

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

   9. Taylor expanded in b around 0 55.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot y\right) + 0.5 \cdot y\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot 0.5 + 0.16666666666666666 \cdot \left(y \cdot b\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.3% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.85 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 9e-232)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 3.85e-177)
     (/ (/ (+ (/ x a) (/ (- (/ x (* a b)) (/ x a)) b)) b) y)
     (/
      (/
       x
       (+ a (* b (+ a (* b (+ (* (* a b) 0.16666666666666666) (* a 0.5)))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 9e-232) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 3.85e-177) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 9d-232) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 3.85d-177) then
        tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
    else
        tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666d0) + (a * 0.5d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 9e-232) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 3.85e-177) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 9e-232:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 3.85e-177:
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
	else:
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 9e-232)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 3.85e-177)
		tmp = Float64(Float64(Float64(Float64(x / a) + Float64(Float64(Float64(x / Float64(a * b)) - Float64(x / a)) / b)) / b) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(Float64(a * b) * 0.16666666666666666) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 9e-232)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 3.85e-177)
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	else
		tmp = (x / (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 9e-232], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.85e-177], N[(N[(N[(N[(x / a), $MachinePrecision] + N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(N[(a * b), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 8.99999999999999933e-232

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. div-exp 72.6%

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

      2. exp-to-pow 73.3%

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

      3. sub-neg 73.3%

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

      4. metadata-eval 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around 0 60.0%

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

   7. Taylor expanded in b around 0 41.6%

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

   8. Taylor expanded in x around 0 52.0%

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

   if 8.99999999999999933e-232 < b < 3.8500000000000001e-177

   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. Add Preprocessing

   3. Taylor expanded in y around 0 68.8%

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

      1. div-exp 68.8%

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

      2. exp-to-pow 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around 0 14.4%

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

   7. Taylor expanded in b around 0 14.4%

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

   8. Taylor expanded in b around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. neg-mul-1 57.6%

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

      3. +-commutative 57.6%

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

      4. sub-neg 57.6%

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

      5. distribute-neg-frac2 57.6%

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

   10. Simplified 57.6%

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

   if 3.8500000000000001e-177 < b

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.4%

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

      1. div-exp 81.7%

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

      2. exp-to-pow 82.7%

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

      3. sub-neg 82.7%

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

      4. metadata-eval 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in t around 0 71.2%

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

   7. Taylor expanded in b around 0 60.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 9 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.85 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.4% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.6 \cdot 10^{-230}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6.6e-230)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 2.7e-176)
     (/ (/ (+ (/ x a) (/ (- (/ x (* a b)) (/ x a)) b)) b) y)
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.6e-230) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 2.7e-176) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6.6d-230) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 2.7d-176) then
        tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.6e-230) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 2.7e-176) {
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6.6e-230:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 2.7e-176:
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6.6e-230)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 2.7e-176)
		tmp = Float64(Float64(Float64(Float64(x / a) + Float64(Float64(Float64(x / Float64(a * b)) - Float64(x / a)) / b)) / b) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6.6e-230)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 2.7e-176)
		tmp = (((x / a) + (((x / (a * b)) - (x / a)) / b)) / b) / y;
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6.6e-230], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.7e-176], N[(N[(N[(N[(x / a), $MachinePrecision] + N[(N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 6.59999999999999987e-230

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. div-exp 72.6%

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

      2. exp-to-pow 73.3%

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

      3. sub-neg 73.3%

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

      4. metadata-eval 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around 0 60.0%

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

   7. Taylor expanded in b around 0 41.6%

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

   8. Taylor expanded in x around 0 52.0%

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

   if 6.59999999999999987e-230 < b < 2.6999999999999998e-176

   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. Add Preprocessing

   3. Taylor expanded in y around 0 68.8%

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

      1. div-exp 68.8%

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

      2. exp-to-pow 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around 0 14.4%

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

   7. Taylor expanded in b around 0 14.4%

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

   8. Taylor expanded in b around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. neg-mul-1 57.6%

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

      3. +-commutative 57.6%

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

      4. sub-neg 57.6%

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

      5. distribute-neg-frac2 57.6%

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

   10. Simplified 57.6%

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

   if 2.6999999999999998e-176 < b

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 88.4%

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

      1. div-exp 81.7%

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

      2. exp-to-pow 82.7%

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

      3. sub-neg 82.7%

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

      4. metadata-eval 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in t around 0 71.2%

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

   7. Taylor expanded in b around 0 55.2%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6.6 \cdot 10^{-230}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;\frac{\frac{\frac{x}{a} + \frac{\frac{x}{a \cdot b} - \frac{x}{a}}{b}}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.3% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e-232)
   (/ (+ (/ x a) (* b (* (/ (* x b) a) 0.5))) y)
   (if (<= b 2.3e-51)
     (/ x (* a (+ y (* b (* b (+ (* y 0.5) (/ y b)))))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e-232) {
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	} else if (b <= 2.3e-51) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.2d-232)) then
        tmp = ((x / a) + (b * (((x * b) / a) * 0.5d0))) / y
    else if (b <= 2.3d-51) then
        tmp = x / (a * (y + (b * (b * ((y * 0.5d0) + (y / b))))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e-232) {
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	} else if (b <= 2.3e-51) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e-232:
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y
	elif b <= 2.3e-51:
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e-232)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(Float64(x * b) / a) * 0.5))) / y);
	elseif (b <= 2.3e-51)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(b * Float64(Float64(y * 0.5) + Float64(y / b)))))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.2e-232)
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	elseif (b <= 2.3e-51)
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e-232], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.3e-51], N[(x / N[(a * N[(y + N[(b * N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999999e-232

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. div-exp 74.6%

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

      2. exp-to-pow 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 66.4%

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

   7. Taylor expanded in b around 0 43.8%

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

   8. Taylor expanded in b around inf 43.4%

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

      1. distribute-rgt-out 50.8%

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

      2. metadata-eval 50.8%

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

      3. associate-*r* 50.8%

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

      4. associate-/l* 52.3%

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

      5. *-commutative 52.3%

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

      6. associate-*r* 52.3%

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

      7. metadata-eval 52.3%

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

      8. *-commutative 52.3%

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

   10. Simplified 52.3%

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

   if -1.19999999999999999e-232 < b < 2.30000000000000002e-51

   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* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 85.2%

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

      4. associate-/l* 82.8%

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

      5. *-commutative 82.8%

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

      6. exp-to-pow 82.8%

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

      7. exp-diff 82.8%

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

      8. *-commutative 82.8%

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

      9. exp-to-pow 84.4%

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

      10. sub-neg 84.4%

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

      11. metadata-eval 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around 0 68.6%

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

      1. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 41.0%

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

   9. Taylor expanded in b around 0 41.0%

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

   10. Taylor expanded in b around inf 46.6%

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

   if 2.30000000000000002e-51 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. div-exp 79.7%

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

      2. exp-to-pow 79.9%

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

      3. sub-neg 79.9%

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

      4. metadata-eval 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in t around 0 80.2%

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

   7. Taylor expanded in b around 0 57.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.3% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 10^{-51}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e-232)
   (/ (+ (/ x a) (* b (- (/ (* x b) a) (/ x a)))) y)
   (if (<= b 1e-51)
     (/ x (* a (+ y (* b (* b (+ (* y 0.5) (/ y b)))))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e-232) {
		tmp = ((x / a) + (b * (((x * b) / a) - (x / a)))) / y;
	} else if (b <= 1e-51) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.2d-232)) then
        tmp = ((x / a) + (b * (((x * b) / a) - (x / a)))) / y
    else if (b <= 1d-51) then
        tmp = x / (a * (y + (b * (b * ((y * 0.5d0) + (y / b))))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e-232) {
		tmp = ((x / a) + (b * (((x * b) / a) - (x / a)))) / y;
	} else if (b <= 1e-51) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e-232:
		tmp = ((x / a) + (b * (((x * b) / a) - (x / a)))) / y
	elif b <= 1e-51:
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e-232)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(Float64(x * b) / a) - Float64(x / a)))) / y);
	elseif (b <= 1e-51)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(b * Float64(Float64(y * 0.5) + Float64(y / b)))))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.2e-232)
		tmp = ((x / a) + (b * (((x * b) / a) - (x / a)))) / y;
	elseif (b <= 1e-51)
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e-232], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1e-51], N[(x / N[(a * N[(y + N[(b * N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999999e-232

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. div-exp 74.6%

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

      2. exp-to-pow 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 66.4%

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

   7. Taylor expanded in b around 0 24.2%

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

   8. Taylor expanded in b around 0 52.6%

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

   if -1.19999999999999999e-232 < b < 1e-51

   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* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 85.2%

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

      4. associate-/l* 82.8%

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

      5. *-commutative 82.8%

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

      6. exp-to-pow 82.8%

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

      7. exp-diff 82.8%

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

      8. *-commutative 82.8%

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

      9. exp-to-pow 84.4%

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

      10. sub-neg 84.4%

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

      11. metadata-eval 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around 0 68.6%

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

      1. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 41.0%

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

   9. Taylor expanded in b around 0 41.0%

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

   10. Taylor expanded in b around inf 46.6%

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

   if 1e-51 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. div-exp 79.7%

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

      2. exp-to-pow 79.9%

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

      3. sub-neg 79.9%

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

      4. metadata-eval 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in t around 0 80.2%

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

   7. Taylor expanded in b around 0 57.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 10^{-51}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.3% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.06e-232)
   (/ (* x (+ (/ 1.0 a) (* b (+ (* 0.5 (/ b a)) (/ -1.0 a))))) y)
   (if (<= b 5e-46)
     (/ x (* a (+ y (* b (* b (+ (* y 0.5) (/ y b)))))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.06e-232) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 5e-46) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.06d-232)) then
        tmp = (x * ((1.0d0 / a) + (b * ((0.5d0 * (b / a)) + ((-1.0d0) / a))))) / y
    else if (b <= 5d-46) then
        tmp = x / (a * (y + (b * (b * ((y * 0.5d0) + (y / b))))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.06e-232) {
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	} else if (b <= 5e-46) {
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.06e-232:
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y
	elif b <= 5e-46:
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.06e-232)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) + Float64(b * Float64(Float64(0.5 * Float64(b / a)) + Float64(-1.0 / a))))) / y);
	elseif (b <= 5e-46)
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(b * Float64(Float64(y * 0.5) + Float64(y / b)))))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.06e-232)
		tmp = (x * ((1.0 / a) + (b * ((0.5 * (b / a)) + (-1.0 / a))))) / y;
	elseif (b <= 5e-46)
		tmp = x / (a * (y + (b * (b * ((y * 0.5) + (y / b))))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.06e-232], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / a), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5e-46], N[(x / N[(a * N[(y + N[(b * N[(b * N[(N[(y * 0.5), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05999999999999994e-232

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. div-exp 74.6%

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

      2. exp-to-pow 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 66.4%

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

   7. Taylor expanded in b around 0 43.8%

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

   8. Taylor expanded in x around 0 55.4%

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

   if -1.05999999999999994e-232 < b < 4.99999999999999992e-46

   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* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 84.3%

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

      4. associate-/l* 82.0%

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

      5. *-commutative 82.0%

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

      6. exp-to-pow 82.0%

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

      7. exp-diff 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 83.6%

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

      10. sub-neg 83.6%

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

      11. metadata-eval 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in t around 0 68.2%

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

      1. associate-/r* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in y around 0 40.1%

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

   9. Taylor expanded in b around 0 40.1%

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

   10. Taylor expanded in b around inf 45.6%

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

   if 4.99999999999999992e-46 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 90.3%

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

      1. div-exp 80.6%

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

      2. exp-to-pow 80.8%

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

      3. sub-neg 80.8%

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

      4. metadata-eval 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in t around 0 82.7%

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

   7. Taylor expanded in b around 0 59.3%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} + b \cdot \left(0.5 \cdot \frac{b}{a} + \frac{-1}{a}\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(b \cdot \left(y \cdot 0.5 + \frac{y}{b}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.1% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.2 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.2e-257)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.2e-257) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.2d-257) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.2e-257) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.2e-257:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.2e-257)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.2e-257)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.2e-257], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.20000000000000008e-257

   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. Add Preprocessing

   3. Taylor expanded in y around 0 80.6%

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

      1. div-exp 72.5%

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

      2. exp-to-pow 73.1%

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

      3. sub-neg 73.1%

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

      4. metadata-eval 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 61.5%

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

   7. Taylor expanded in b around 0 47.3%

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

   if 1.20000000000000008e-257 < b

   1. Initial program 98.9%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 81.3%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 77.9%

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

      8. *-commutative 77.9%

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

      9. exp-to-pow 78.9%

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

      10. sub-neg 78.9%

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

      11. metadata-eval 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in t around 0 67.7%

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

      1. associate-/r* 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in y around 0 61.6%

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

   9. Taylor expanded in b around 0 43.7%

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

   10. Taylor expanded in y around 0 47.0%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.2 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.9% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.05e+42)
   (/ (+ (/ x a) (* b (* (/ (* x b) a) 0.5))) y)
   (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.05e+42) {
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.05d+42) then
        tmp = ((x / a) + (b * (((x * b) / a) * 0.5d0))) / y
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.05e+42) {
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.05e+42:
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.05e+42)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(Float64(x * b) / a) * 0.5))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.05e+42)
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.05e+42], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.04999999999999998e42

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 79.8%

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

      1. div-exp 74.6%

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

      2. exp-to-pow 75.5%

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

      3. sub-neg 75.5%

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

      4. metadata-eval 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in t around 0 55.3%

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

   7. Taylor expanded in b around 0 37.0%

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

   8. Taylor expanded in b around inf 36.7%

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

      1. distribute-rgt-out 44.3%

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

      2. metadata-eval 44.3%

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

      3. associate-*r* 44.3%

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

      4. associate-/l* 45.0%

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

      5. *-commutative 45.0%

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

      6. associate-*r* 45.0%

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

      7. metadata-eval 45.0%

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

      8. *-commutative 45.0%

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

   10. Simplified 45.0%

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

   if 1.04999999999999998e42 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 71.4%

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

      4. associate-/l* 71.4%

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

      5. *-commutative 71.4%

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

      6. exp-to-pow 71.4%

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

      7. exp-diff 64.3%

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

      8. *-commutative 64.3%

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

      9. exp-to-pow 64.3%

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

      10. sub-neg 64.3%

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

      11. metadata-eval 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in t around 0 69.1%

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

      1. associate-/r* 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in y around 0 90.6%

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

   9. Taylor expanded in b around 0 60.9%

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

   10. Taylor expanded in y around 0 70.0%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.8% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.4e+21)
   (/ (+ (/ x a) (* b (* (/ (* x b) a) 0.5))) y)
   (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+21) {
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.4d+21)) then
        tmp = ((x / a) + (b * (((x * b) / a) * 0.5d0))) / y
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+21) {
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.4e+21:
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.4e+21)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(Float64(x * b) / a) * 0.5))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.4e+21)
		tmp = ((x / a) + (b * (((x * b) / a) * 0.5))) / y;
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.4e+21], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4e21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.4%

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

      1. div-exp 75.1%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 88.6%

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

   7. Taylor expanded in b around 0 51.3%

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

   8. Taylor expanded in b around inf 51.3%

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

      1. distribute-rgt-out 59.0%

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

      2. metadata-eval 59.0%

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

      3. associate-*r* 59.0%

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

      4. associate-/l* 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-*r* 62.0%

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

      7. metadata-eval 62.0%

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

      8. *-commutative 62.0%

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

   10. Simplified 62.0%

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

   if -3.4e21 < b

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 79.7%

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

      1. div-exp 75.8%

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

      2. exp-to-pow 76.7%

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

      3. sub-neg 76.7%

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

      4. metadata-eval 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 54.1%

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

   7. Taylor expanded in b around 0 46.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(\frac{x \cdot b}{a} \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.8% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.2e-149)
   (/ (- x (* b (+ x (* b (* x -0.5))))) (* y a))
   (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e-149) {
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.2d-149)) then
        tmp = (x - (b * (x + (b * (x * (-0.5d0)))))) / (y * a)
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e-149) {
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.2e-149:
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a)
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.2e-149)
		tmp = Float64(Float64(x - Float64(b * Float64(x + Float64(b * Float64(x * -0.5))))) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.2e-149)
		tmp = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.2e-149], N[(N[(x - N[(b * N[(x + N[(b * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.20000000000000013e-149

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. div-exp 71.7%

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

      2. exp-to-pow 71.8%

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

      3. sub-neg 71.8%

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

      4. metadata-eval 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in t around 0 66.9%

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

   7. Taylor expanded in b around 0 43.6%

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

   8. Taylor expanded in a around 0 51.0%

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

      1. associate-*r* 51.0%

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

      2. mul-1-neg 51.0%

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

      3. distribute-rgt-out 51.0%

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

      4. metadata-eval 51.0%

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

   10. Simplified 51.0%

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

   if -8.20000000000000013e-149 < b

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 81.5%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 79.0%

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

      3. sub-neg 79.0%

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

      4. metadata-eval 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in t around 0 57.9%

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

   7. Taylor expanded in b around 0 49.1%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.5% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e-149)
   (- (/ x (* y a)) (* (/ x a) (/ b y)))
   (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-149) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d-149)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-149) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e-149:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e-149)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e-149)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e-149], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999968e-149

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. associate--l+ 99.6%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 77.9%

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

      5. *-commutative 77.9%

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

      6. exp-to-pow 77.9%

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

      7. exp-diff 68.1%

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

      8. *-commutative 68.1%

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

      9. exp-to-pow 68.4%

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

      10. sub-neg 68.4%

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

      11. metadata-eval 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in t around 0 67.8%

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

      1. associate-/r* 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in y around 0 67.8%

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

   9. Taylor expanded in b around 0 42.4%

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

       1. +-commutative 42.4%

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

       2. mul-1-neg 42.4%

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

       3. unsub-neg 42.4%

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

       4. *-commutative 42.4%

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

       5. *-commutative 42.4%

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

       6. times-frac 38.5%

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

   11. Simplified 38.5%

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

   if -4.99999999999999968e-149 < b

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 81.5%

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

      1. div-exp 77.8%

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

      2. exp-to-pow 79.0%

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

      3. sub-neg 79.0%

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

      4. metadata-eval 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in t around 0 57.9%

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

   7. Taylor expanded in b around 0 40.2%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 42.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.25 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.25e-257)
   (/ (* (/ x a) (- 1.0 b)) y)
   (/ x (* a (+ y (* b (* y (* b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.25e-257) {
		tmp = ((x / a) * (1.0 - b)) / y;
	} else {
		tmp = x / (a * (y + (b * (y * (b * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.25d-257) then
        tmp = ((x / a) * (1.0d0 - b)) / y
    else
        tmp = x / (a * (y + (b * (y * (b * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.25e-257) {
		tmp = ((x / a) * (1.0 - b)) / y;
	} else {
		tmp = x / (a * (y + (b * (y * (b * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.25e-257:
		tmp = ((x / a) * (1.0 - b)) / y
	else:
		tmp = x / (a * (y + (b * (y * (b * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.25e-257)
		tmp = Float64(Float64(Float64(x / a) * Float64(1.0 - b)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y * Float64(b * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.25e-257)
		tmp = ((x / a) * (1.0 - b)) / y;
	else
		tmp = x / (a * (y + (b * (y * (b * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.25e-257], N[(N[(N[(x / a), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.24999999999999997e-257

   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. Add Preprocessing

   3. Taylor expanded in y around 0 80.6%

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

      1. div-exp 72.5%

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

      2. exp-to-pow 73.1%

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

      3. sub-neg 73.1%

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

      4. metadata-eval 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 61.5%

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

   7. Taylor expanded in b around 0 28.2%

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

   8. Taylor expanded in b around 0 47.3%

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

      1. *-rgt-identity 47.3%

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

      2. cancel-sign-sub 47.3%

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

      3. mul-1-neg 47.3%

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

      4. associate-/l* 41.0%

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

      5. distribute-rgt-neg-out 41.0%

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

      6. *-commutative 41.0%

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

      7. distribute-lft-out-- 41.8%

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

      8. distribute-neg-frac 41.8%

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

   10. Simplified 41.8%

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

   if 1.24999999999999997e-257 < b

   1. Initial program 98.9%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 81.3%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 77.9%

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

      8. *-commutative 77.9%

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

      9. exp-to-pow 78.9%

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

      10. sub-neg 78.9%

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

      11. metadata-eval 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in t around 0 67.7%

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

      1. associate-/r* 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in y around 0 61.6%

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

   9. Taylor expanded in b around 0 43.7%

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

   10. Taylor expanded in b around inf 43.7%

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

       1. *-commutative 43.7%

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

       2. associate-*r* 43.7%

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

       3. *-commutative 43.7%

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

       4. associate-*r* 43.7%

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

   12. Simplified 43.7%

       \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \color{blue}{\left(y \cdot \left(0.5 \cdot b\right)\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.25 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 43.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.1 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.1e-257)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (/ x (* a (+ y (* b (* y (* b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.1e-257) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y + (b * (y * (b * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.1d-257) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (a * (y + (b * (y * (b * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.1e-257) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y + (b * (y * (b * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.1e-257:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (a * (y + (b * (y * (b * 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.1e-257)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y * Float64(b * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.1e-257)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (a * (y + (b * (y * (b * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.1e-257], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.09999999999999994e-257

   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. Add Preprocessing

   3. Taylor expanded in y around 0 80.6%

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

      1. div-exp 72.5%

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

      2. exp-to-pow 73.1%

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

      3. sub-neg 73.1%

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

      4. metadata-eval 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 61.5%

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

   7. Taylor expanded in b around 0 47.3%

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

   if 1.09999999999999994e-257 < b

   1. Initial program 98.9%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 81.3%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 77.9%

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

      8. *-commutative 77.9%

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

      9. exp-to-pow 78.9%

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

      10. sub-neg 78.9%

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

      11. metadata-eval 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in t around 0 67.7%

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

      1. associate-/r* 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in y around 0 61.6%

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

   9. Taylor expanded in b around 0 43.7%

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

   10. Taylor expanded in b around inf 43.7%

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

       1. *-commutative 43.7%

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

       2. associate-*r* 43.7%

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

       3. *-commutative 43.7%

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

       4. associate-*r* 43.7%

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

   12. Simplified 43.7%

       \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \color{blue}{\left(y \cdot \left(0.5 \cdot b\right)\right)}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.1 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y \cdot \left(b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.2% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6 \cdot 10^{-55}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 6e-55) (/ 1.0 (* a (/ y x))) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 6e-55) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 6d-55) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 6e-55) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 6e-55:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 6e-55)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 6e-55)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 6e-55], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.00000000000000033e-55

   1. Initial program 99.2%

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

      1. associate-/l* 98.3%

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

      2. associate--l+ 98.3%

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

      3. exp-sum 77.5%

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

      4. associate-/l* 77.5%

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

      5. *-commutative 77.5%

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

      6. exp-to-pow 77.5%

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

      7. exp-diff 69.2%

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

      8. *-commutative 69.2%

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

      9. exp-to-pow 69.8%

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

      10. sub-neg 69.8%

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

      11. metadata-eval 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in t around 0 74.3%

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

      1. associate-/r* 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 54.4%

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

   9. Taylor expanded in b around 0 29.3%

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

       1. *-commutative 29.3%

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

   11. Simplified 29.3%

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

       1. clear-num 29.3%

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

       2. inv-pow 29.3%

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

       3. *-commutative 29.3%

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

   13. Applied egg-rr 29.3%

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

       1. unpow-1 29.3%

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

       2. associate-/l* 34.2%

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

   15. Simplified 34.2%

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

   if 6.00000000000000033e-55 < a

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. div-exp 81.0%

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

      2. exp-to-pow 81.9%

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

      3. sub-neg 81.9%

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

      4. metadata-eval 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in t around 0 62.8%

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

   7. Taylor expanded in b around 0 36.4%

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

   8. Taylor expanded in x around 0 37.6%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6 \cdot 10^{-55}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 35.9% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2800000:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2800000.0) (/ 1.0 (* a (/ y x))) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2800000.0) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2800000.0d0)) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2800000.0) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2800000.0:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2800000.0)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2800000.0)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2800000.0], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8e6

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. exp-diff 58.9%

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

      8. *-commutative 58.9%

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

      9. exp-to-pow 58.9%

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

      10. sub-neg 58.9%

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

      11. metadata-eval 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in t around 0 73.3%

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

      1. associate-/r* 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in y around 0 87.7%

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

   9. Taylor expanded in b around 0 23.9%

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

       1. *-commutative 23.9%

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

   11. Simplified 23.9%

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

       1. clear-num 23.9%

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

       2. inv-pow 23.9%

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

       3. *-commutative 23.9%

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

   13. Applied egg-rr 23.9%

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

       1. unpow-1 23.9%

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

       2. associate-/l* 27.2%

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

   15. Simplified 27.2%

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

   if -2.8e6 < b

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 79.8%

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

      1. div-exp 76.3%

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

      2. exp-to-pow 77.3%

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

      3. sub-neg 77.3%

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

      4. metadata-eval 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0 53.7%

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

   7. Taylor expanded in b around 0 39.1%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2800000:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.8% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.45e-148) (* (/ x (* y a)) (- 1.0 b)) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e-148) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.45d-148)) then
        tmp = (x / (y * a)) * (1.0d0 - b)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e-148) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.45e-148:
		tmp = (x / (y * a)) * (1.0 - b)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.45e-148)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(1.0 - b));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.45e-148)
		tmp = (x / (y * a)) * (1.0 - b);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.45e-148], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4499999999999999e-148

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 71.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 71.8%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 71.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 71.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 71.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 66.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 17.3%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   8. Taylor expanded in b around 0 42.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   9. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

      2. remove-double-neg 42.4%

         \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

      3. distribute-neg-out 42.4%

         \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

      4. sub-neg 42.4%

         \[\leadsto -\color{blue}{\left(\frac{b \cdot x}{a \cdot y} - \frac{x}{a \cdot y}\right)} \]

      5. associate-/l* 35.4%

         \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} - \frac{x}{a \cdot y}\right) \]

      6. *-lft-identity 35.4%

         \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} - \color{blue}{1 \cdot \frac{x}{a \cdot y}}\right) \]

      7. distribute-rgt-out-- 35.4%

         \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b - 1\right)} \]

   10. Simplified 35.4%

       \[\leadsto \color{blue}{-\frac{x}{a \cdot y} \cdot \left(b - 1\right)} \]

   if -1.4499999999999999e-148 < b

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 77.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 79.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 79.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 79.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 79.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 57.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 40.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 39.1% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.46 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.46e-12) (/ (* (/ x a) (- 1.0 b)) y) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.46e-12) {
		tmp = ((x / a) * (1.0 - b)) / y;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.46d-12) then
        tmp = ((x / a) * (1.0d0 - b)) / y
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.46e-12) {
		tmp = ((x / a) * (1.0 - b)) / y;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.46e-12:
		tmp = ((x / a) * (1.0 - b)) / y
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.46e-12)
		tmp = Float64(Float64(Float64(x / a) * Float64(1.0 - b)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.46e-12)
		tmp = ((x / a) * (1.0 - b)) / y;
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.46e-12], N[(N[(N[(x / a), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.46000000000000004e-12

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 74.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 75.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 75.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 75.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 75.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 54.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 31.8%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   8. Taylor expanded in b around 0 43.4%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. *-rgt-identity 43.4%

         \[\leadsto \frac{-1 \cdot \frac{b \cdot x}{a} + \color{blue}{\frac{x}{a} \cdot 1}}{y} \]

      2. cancel-sign-sub 43.4%

         \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} - \left(-\frac{x}{a}\right) \cdot 1}}{y} \]

      3. mul-1-neg 43.4%

         \[\leadsto \frac{\color{blue}{\left(-\frac{b \cdot x}{a}\right)} - \left(-\frac{x}{a}\right) \cdot 1}{y} \]

      4. associate-/l* 38.1%

         \[\leadsto \frac{\left(-\color{blue}{b \cdot \frac{x}{a}}\right) - \left(-\frac{x}{a}\right) \cdot 1}{y} \]

      5. distribute-rgt-neg-out 38.1%

         \[\leadsto \frac{\color{blue}{b \cdot \left(-\frac{x}{a}\right)} - \left(-\frac{x}{a}\right) \cdot 1}{y} \]

      6. *-commutative 38.1%

         \[\leadsto \frac{\color{blue}{\left(-\frac{x}{a}\right) \cdot b} - \left(-\frac{x}{a}\right) \cdot 1}{y} \]

      7. distribute-lft-out-- 41.1%

         \[\leadsto \frac{\color{blue}{\left(-\frac{x}{a}\right) \cdot \left(b - 1\right)}}{y} \]

      8. distribute-neg-frac 41.1%

         \[\leadsto \frac{\color{blue}{\frac{-x}{a}} \cdot \left(b - 1\right)}{y} \]

   10. Simplified 41.1%

       \[\leadsto \frac{\color{blue}{\frac{-x}{a} \cdot \left(b - 1\right)}}{y} \]

   if 1.46000000000000004e-12 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 89.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 78.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 78.8%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 78.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 78.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 78.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 84.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 32.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   8. Taylor expanded in b around inf 34.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.46 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 34.6% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.2e+105) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.2e+105) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.2d+105) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.2e+105) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.2e+105:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.2e+105)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.2e+105)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.2e+105], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.2000000000000004e105

   1. Initial program 98.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 75.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 76.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 76.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 76.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 76.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 57.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 34.8%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 5.2000000000000004e105 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 94.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 78.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 78.8%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 78.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 78.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 78.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 88.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 38.4%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   8. Taylor expanded in b around inf 38.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 35.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7e+36) (/ (/ x a) y) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7e+36) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7d+36) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7e+36) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7e+36:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7e+36)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7e+36)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7e+36], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.9999999999999996e36

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 74.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 75.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 75.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 75.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 75.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 54.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 35.3%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 6.9999999999999996e36 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 95.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 82.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 82.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 82.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 82.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 82.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 91.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 35.4%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   8. Taylor expanded in b around inf 33.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 35.4%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

   10. Simplified 35.4%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot b\right) \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 35.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.5e-82) (/ 1.0 (* a (/ y x))) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.5e-82) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.5d-82) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = (x / (a * b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.5e-82) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.5e-82:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.5e-82)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.5e-82)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.5e-82], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.4999999999999997e-82

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 75.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 75.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 76.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 76.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 76.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.1%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 71.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 71.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 54.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 35.2%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 35.2%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   12. Step-by-step derivation

       1. clear-num 35.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. inv-pow 35.2%

          \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

       3. *-commutative 35.2%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot y}}{x}\right)}^{-1} \]

   13. Applied egg-rr 35.2%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 35.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 36.6%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 36.6%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if 7.4999999999999997e-82 < b

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 89.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 80.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 80.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 80.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 80.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 80.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 74.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 34.1%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   8. Taylor expanded in b around inf 34.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 30.7% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.7%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 80.0%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 79.2%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 79.2%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 79.2%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 74.5%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 74.5%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 75.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 75.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 75.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 75.3%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 68.9%

   \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
6. Step-by-step derivation

   1. associate-/r* 70.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

7. Simplified 70.8%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

8. Taylor expanded in y around 0 60.4%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 30.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 30.8%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

11. Simplified 30.8%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

12. Final simplification 30.8%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Alternative 32: 30.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 82.3%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
4. Step-by-step derivation

   1. div-exp 75.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   2. exp-to-pow 76.4%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   3. sub-neg 76.4%

      \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

   4. metadata-eval 76.4%

      \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

5. Simplified 76.4%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

6. Taylor expanded in t around 0 61.1%

   \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

7. Taylor expanded in b around 0 32.6%

   \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

8. Final simplification 32.6%

   \[\leadsto \frac{\frac{x}{a}}{y} \]
9. Add Preprocessing

Developer target: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (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))