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

Percentage Accurate: 98.3% → 98.3%

Time: 28.3s

Alternatives: 21

Speedup: 1.0×

• 47.9% 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: 98.3% 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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+248}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+248)
   (* x (/ (pow a t) (* y a)))
   (if (<= (+ t -1.0) 2e+36)
     (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
     (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+248) {
		tmp = x * (pow(a, t) / (y * a));
	} else if ((t + -1.0) <= 2e+36) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-5d+248)) then
        tmp = x * ((a ** t) / (y * a))
    else if ((t + (-1.0d0)) <= 2d+36) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+248) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if ((t + -1.0) <= 2e+36) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+248:
		tmp = x * (math.pow(a, t) / (y * a))
	elif (t + -1.0) <= 2e+36:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+248)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (Float64(t + -1.0) <= 2e+36)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+248)
		tmp = x * ((a ^ t) / (y * a));
	elseif ((t + -1.0) <= 2e+36)
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+248], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+36], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -4.9999999999999996e248

   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. exp-diff 64.3%

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

      3. associate-/l/ 64.3%

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

      4. exp-sum 64.3%

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

      5. times-frac 64.3%

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

      6. *-commutative 64.3%

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

      7. exp-to-pow 64.3%

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

      8. *-commutative 64.3%

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

      9. exp-to-pow 64.3%

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

      10. sub-neg 64.3%

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

      11. metadata-eval 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in y around 0 64.3%

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

      1. associate-/l* 64.3%

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

      2. exp-to-pow 64.3%

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

      3. sub-neg 64.3%

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

      4. metadata-eval 64.3%

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

   7. Simplified 64.3%

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

      1. unpow-prod-up 64.3%

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

      2. times-frac 64.3%

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

      3. unpow-1 64.3%

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

   9. Applied egg-rr 64.3%

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

       1. associate-/l/ 64.3%

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

       2. *-commutative 64.3%

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

       3. associate-*r/ 64.3%

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

   11. Simplified 64.3%

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

   12. Taylor expanded in b around 0 100.0%

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

   if -4.9999999999999996e248 < (-.f64 t 1) < 2.00000000000000008e36

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   if 2.00000000000000008e36 < (-.f64 t 1)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.3%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+248}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+55} \lor \neg \left(y \leq 2.9 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+55) (not (<= y 2.9e+31)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+55) || !(y <= 2.9e+31)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.1d+55)) .or. (.not. (y <= 2.9d+31))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+55) || !(y <= 2.9e+31)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e+55) or not (y <= 2.9e+31):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e+55) || !(y <= 2.9e+31))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e+55) || ~((y <= 2.9e+31)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e+55], N[Not[LessEqual[y, 2.9e+31]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000005e55 or 2.9e31 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in b around 0 88.0%

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

      1. div-exp 88.0%

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

      2. *-commutative 88.0%

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

      3. exp-to-pow 88.0%

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

      4. rem-exp-log 88.0%

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

   8. Simplified 88.0%

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

   if -1.10000000000000005e55 < y < 2.9e31

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 94.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+55} \lor \neg \left(y \leq 2.9 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+53} \lor \neg \left(y \leq 2.3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.2e+53) (not (<= y 2.3e+27)))
   (/ (* x (/ (pow z y) a)) y)
   (* x (/ (/ (pow a t) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.2e+53) || !(y <= 2.3e+27)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * ((pow(a, t) / a) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.2d+53)) .or. (.not. (y <= 2.3d+27))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x * (((a ** t) / a) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.2e+53) || !(y <= 2.3e+27)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x * ((Math.pow(a, t) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.2e+53) or not (y <= 2.3e+27):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x * ((math.pow(a, t) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.2e+53) || !(y <= 2.3e+27))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.2e+53) || ~((y <= 2.3e+27)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x * (((a ^ t) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.2e+53], N[Not[LessEqual[y, 2.3e+27]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999999e53 or 2.3000000000000001e27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. mul-1-neg 92.1%

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

      3. unsub-neg 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in b around 0 87.3%

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

      1. div-exp 87.3%

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

      2. *-commutative 87.3%

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

      3. exp-to-pow 87.3%

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

      4. rem-exp-log 87.3%

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

   8. Simplified 87.3%

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

   if -2.19999999999999999e53 < y < 2.3000000000000001e27

   1. Initial program 96.7%

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

      1. associate-/l* 97.6%

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

      2. exp-diff 82.5%

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

      3. associate-/l/ 82.5%

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

      4. exp-sum 80.2%

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

      5. times-frac 80.2%

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

      6. *-commutative 80.2%

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

      7. exp-to-pow 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 81.0%

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

      10. sub-neg 81.0%

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

      11. metadata-eval 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around 0 81.1%

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

      1. associate-/l* 84.3%

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

      2. exp-to-pow 84.9%

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

      3. sub-neg 84.9%

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

      4. metadata-eval 84.9%

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

   7. Simplified 84.9%

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

      1. unpow-prod-up 85.0%

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

      2. unpow-1 85.0%

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

   9. Applied egg-rr 85.0%

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

       1. associate-*r/ 85.0%

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

       2. *-rgt-identity 85.0%

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

   11. Simplified 85.0%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+53} \lor \neg \left(y \leq 2.3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= t -2.7e+242)
     (* x (/ (pow a t) (* y a)))
     (if (<= t -7.5e-26)
       t_1
       (if (<= t 1.25e-294)
         (/ x (* a (* y (exp b))))
         (if (<= t 2.12e+36) t_1 (* x (/ (pow a (+ t -1.0)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (t <= -2.7e+242) {
		tmp = x * (pow(a, t) / (y * a));
	} else if (t <= -7.5e-26) {
		tmp = t_1;
	} else if (t <= 1.25e-294) {
		tmp = x / (a * (y * exp(b)));
	} else if (t <= 2.12e+36) {
		tmp = t_1;
	} else {
		tmp = x * (pow(a, (t + -1.0)) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (t <= (-2.7d+242)) then
        tmp = x * ((a ** t) / (y * a))
    else if (t <= (-7.5d-26)) then
        tmp = t_1
    else if (t <= 1.25d-294) then
        tmp = x / (a * (y * exp(b)))
    else if (t <= 2.12d+36) then
        tmp = t_1
    else
        tmp = x * ((a ** (t + (-1.0d0))) / 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 t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (t <= -2.7e+242) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if (t <= -7.5e-26) {
		tmp = t_1;
	} else if (t <= 1.25e-294) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t <= 2.12e+36) {
		tmp = t_1;
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if t <= -2.7e+242:
		tmp = x * (math.pow(a, t) / (y * a))
	elif t <= -7.5e-26:
		tmp = t_1
	elif t <= 1.25e-294:
		tmp = x / (a * (y * math.exp(b)))
	elif t <= 2.12e+36:
		tmp = t_1
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (t <= -2.7e+242)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (t <= -7.5e-26)
		tmp = t_1;
	elseif (t <= 1.25e-294)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t <= 2.12e+36)
		tmp = t_1;
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (t <= -2.7e+242)
		tmp = x * ((a ^ t) / (y * a));
	elseif (t <= -7.5e-26)
		tmp = t_1;
	elseif (t <= 1.25e-294)
		tmp = x / (a * (y * exp(b)));
	elseif (t <= 2.12e+36)
		tmp = t_1;
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.7e+242], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-26], t$95$1, If[LessEqual[t, 1.25e-294], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.12e+36], t$95$1, N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.69999999999999984e242

   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. exp-diff 64.3%

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

      3. associate-/l/ 64.3%

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

      4. exp-sum 64.3%

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

      5. times-frac 64.3%

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

      6. *-commutative 64.3%

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

      7. exp-to-pow 64.3%

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

      8. *-commutative 64.3%

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

      9. exp-to-pow 64.3%

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

      10. sub-neg 64.3%

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

      11. metadata-eval 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in y around 0 64.3%

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

      1. associate-/l* 64.3%

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

      2. exp-to-pow 64.3%

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

      3. sub-neg 64.3%

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

      4. metadata-eval 64.3%

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

   7. Simplified 64.3%

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

      1. unpow-prod-up 64.3%

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

      2. times-frac 64.3%

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

      3. unpow-1 64.3%

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

   9. Applied egg-rr 64.3%

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

       1. associate-/l/ 64.3%

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

       2. *-commutative 64.3%

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

       3. associate-*r/ 64.3%

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

   11. Simplified 64.3%

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

   12. Taylor expanded in b around 0 100.0%

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

   if -2.69999999999999984e242 < t < -7.4999999999999994e-26 or 1.2500000000000001e-294 < t < 2.12000000000000004e36

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. mul-1-neg 92.1%

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

      3. unsub-neg 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in b around 0 78.3%

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

      1. div-exp 78.3%

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

      2. *-commutative 78.3%

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

      3. exp-to-pow 78.3%

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

      4. rem-exp-log 78.8%

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

   8. Simplified 78.8%

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

   if -7.4999999999999994e-26 < t < 1.2500000000000001e-294

   1. Initial program 95.8%

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

      1. associate-/l* 97.7%

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

      2. exp-diff 76.1%

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

      3. associate-/l/ 76.1%

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

      4. exp-sum 76.2%

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

      5. times-frac 76.2%

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

      6. *-commutative 76.2%

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

      7. exp-to-pow 76.2%

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

      8. *-commutative 76.2%

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

      9. exp-to-pow 76.9%

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

      10. sub-neg 76.9%

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

      11. metadata-eval 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. associate-/l* 79.9%

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

      2. exp-to-pow 80.5%

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

      3. sub-neg 80.5%

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

      4. metadata-eval 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in t around 0 80.5%

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

   if 2.12000000000000004e36 < t

   1. Initial program 100.0%

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

      1. associate-/l* 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. exp-diff 80.7%

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

      3. associate-/l/ 80.7%

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

      4. exp-sum 63.2%

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

      5. times-frac 63.2%

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

      6. *-commutative 63.2%

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

      7. exp-to-pow 63.2%

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

      8. *-commutative 63.2%

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

      9. exp-to-pow 63.2%

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

      10. sub-neg 63.2%

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

      11. metadata-eval 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in y around 0 77.2%

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

      1. associate-/l* 77.2%

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

      2. exp-to-pow 77.2%

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

      3. sub-neg 77.2%

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

      4. metadata-eval 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in b around 0 91.4%

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

      1. remove-double-neg 91.4%

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

      2. log-rec 91.4%

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

      3. distribute-lft-neg-in 91.4%

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

      4. mul-1-neg 91.4%

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

      5. mul-1-neg 91.4%

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

      6. distribute-lft-neg-in 91.4%

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

      7. log-rec 91.4%

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

      8. remove-double-neg 91.4%

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

      9. associate-/l* 91.4%

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

   10. Simplified 91.4%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e-14)
   (* x (/ (pow a t) (* y a)))
   (if (<= t 1.25e-294)
     (/ x (* a (* y (exp b))))
     (if (<= t 2.8e+36)
       (* (/ (pow z y) a) (/ x y))
       (* x (/ (pow a (+ t -1.0)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e-14) {
		tmp = x * (pow(a, t) / (y * a));
	} else if (t <= 1.25e-294) {
		tmp = x / (a * (y * exp(b)));
	} else if (t <= 2.8e+36) {
		tmp = (pow(z, y) / a) * (x / y);
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.5d-14)) then
        tmp = x * ((a ** t) / (y * a))
    else if (t <= 1.25d-294) then
        tmp = x / (a * (y * exp(b)))
    else if (t <= 2.8d+36) then
        tmp = ((z ** y) / a) * (x / y)
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e-14) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if (t <= 1.25e-294) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t <= 2.8e+36) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e-14:
		tmp = x * (math.pow(a, t) / (y * a))
	elif t <= 1.25e-294:
		tmp = x / (a * (y * math.exp(b)))
	elif t <= 2.8e+36:
		tmp = (math.pow(z, y) / a) * (x / y)
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e-14)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (t <= 1.25e-294)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t <= 2.8e+36)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.5e-14)
		tmp = x * ((a ^ t) / (y * a));
	elseif (t <= 1.25e-294)
		tmp = x / (a * (y * exp(b)));
	elseif (t <= 2.8e+36)
		tmp = ((z ^ y) / a) * (x / y);
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e-14], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-294], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+36], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999996e-14

   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. Step-by-step derivation

      1. associate-/l* 99.8%

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

      2. exp-diff 79.8%

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

      3. associate-/l/ 79.8%

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

      4. exp-sum 61.3%

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

      5. times-frac 61.3%

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

      6. *-commutative 61.3%

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

      7. exp-to-pow 61.3%

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

      8. *-commutative 61.3%

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

      9. exp-to-pow 61.3%

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

      10. sub-neg 61.3%

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

      11. metadata-eval 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. associate-/l* 61.5%

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

      2. exp-to-pow 61.5%

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

      3. sub-neg 61.5%

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

      4. metadata-eval 61.5%

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

   7. Simplified 61.5%

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

      1. unpow-prod-up 61.7%

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

      2. times-frac 61.7%

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

      3. unpow-1 61.7%

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

   9. Applied egg-rr 61.7%

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

       1. associate-/l/ 61.7%

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

       2. *-commutative 61.7%

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

       3. associate-*r/ 61.7%

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

   11. Simplified 61.7%

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

   12. Taylor expanded in b around 0 70.5%

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

   if -7.4999999999999996e-14 < t < 1.2500000000000001e-294

   1. Initial program 95.9%

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

      1. associate-/l* 97.7%

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

      2. exp-diff 77.4%

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

      3. associate-/l/ 77.4%

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

      4. exp-sum 77.5%

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

      5. times-frac 77.5%

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

      6. *-commutative 77.5%

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

      7. exp-to-pow 77.5%

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

      8. *-commutative 77.5%

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

      9. exp-to-pow 78.3%

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

      10. sub-neg 78.3%

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

      11. metadata-eval 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. associate-/l* 79.6%

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

      2. exp-to-pow 80.3%

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

      3. sub-neg 80.3%

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

      4. metadata-eval 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in t around 0 80.2%

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

   if 1.2500000000000001e-294 < t < 2.8000000000000001e36

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. mul-1-neg 96.0%

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

      3. unsub-neg 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in b around 0 79.8%

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

      1. div-exp 79.8%

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

      2. *-commutative 79.8%

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

      3. exp-to-pow 79.8%

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

      4. rem-exp-log 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in x around 0 69.0%

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

       1. *-commutative 69.0%

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

       2. times-frac 77.2%

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

   11. Simplified 77.2%

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

   if 2.8000000000000001e36 < t

   1. Initial program 100.0%

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

      1. associate-/l* 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. exp-diff 80.7%

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

      3. associate-/l/ 80.7%

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

      4. exp-sum 63.2%

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

      5. times-frac 63.2%

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

      6. *-commutative 63.2%

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

      7. exp-to-pow 63.2%

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

      8. *-commutative 63.2%

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

      9. exp-to-pow 63.2%

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

      10. sub-neg 63.2%

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

      11. metadata-eval 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in y around 0 77.2%

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

      1. associate-/l* 77.2%

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

      2. exp-to-pow 77.2%

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

      3. sub-neg 77.2%

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

      4. metadata-eval 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in b around 0 91.4%

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

      1. remove-double-neg 91.4%

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

      2. log-rec 91.4%

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

      3. distribute-lft-neg-in 91.4%

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

      4. mul-1-neg 91.4%

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

      5. mul-1-neg 91.4%

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

      6. distribute-lft-neg-in 91.4%

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

      7. log-rec 91.4%

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

      8. remove-double-neg 91.4%

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

      9. associate-/l* 91.4%

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

   10. Simplified 91.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+85} \lor \neg \left(b \leq 6000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.1e+85) (not (<= b 6000.0)))
   (/ x (* a (* y (exp b))))
   (* x (/ (pow a t) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+85) || !(b <= 6000.0)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (pow(a, t) / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.1d+85)) .or. (.not. (b <= 6000.0d0))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * ((a ** t) / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+85) || !(b <= 6000.0)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(a, t) / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.1e+85) or not (b <= 6000.0):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.pow(a, t) / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.1e+85) || !(b <= 6000.0))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.1e+85) || ~((b <= 6000.0)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * ((a ^ t) / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.1e+85], N[Not[LessEqual[b, 6000.0]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1000000000000001e85 or 6e3 < 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. exp-diff 63.5%

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

      3. associate-/l/ 63.5%

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

      4. exp-sum 55.7%

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

      5. times-frac 55.7%

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

      6. *-commutative 55.7%

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

      7. exp-to-pow 55.7%

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

      8. *-commutative 55.7%

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

      9. exp-to-pow 55.7%

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

      10. sub-neg 55.7%

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

      11. metadata-eval 55.7%

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

   3. Simplified 55.7%

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

   5. Taylor expanded in y around 0 61.0%

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

      1. associate-/l* 65.4%

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

      2. exp-to-pow 65.4%

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

      3. sub-neg 65.4%

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

      4. metadata-eval 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in t around 0 83.7%

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

   if -2.1000000000000001e85 < b < 6e3

   1. Initial program 96.9%

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

      1. associate-/l* 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. exp-diff 92.1%

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

      3. associate-/l/ 92.1%

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

      4. exp-sum 79.3%

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

      5. times-frac 79.3%

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

      6. *-commutative 79.3%

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

      7. exp-to-pow 79.4%

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

      8. *-commutative 79.4%

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

      9. exp-to-pow 80.1%

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

      10. sub-neg 80.1%

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

      11. metadata-eval 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in y around 0 68.2%

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

      1. associate-/l* 68.4%

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

      2. exp-to-pow 69.0%

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

      3. sub-neg 69.0%

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

      4. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

      1. unpow-prod-up 69.0%

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

      2. times-frac 69.0%

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

      3. unpow-1 69.0%

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

   9. Applied egg-rr 69.0%

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

       1. associate-/l/ 69.0%

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

       2. *-commutative 69.0%

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

       3. associate-*r/ 69.1%

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

   11. Simplified 69.1%

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

   12. Taylor expanded in b around 0 64.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+85} \lor \neg \left(b \leq 6000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.8e-14)
   (* x (/ (pow a t) (* y a)))
   (if (<= t 4.2e+83)
     (/ x (* a (* y (exp b))))
     (* x (/ (pow a (+ t -1.0)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.8e-14) {
		tmp = x * (pow(a, t) / (y * a));
	} else if (t <= 4.2e+83) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.8d-14)) then
        tmp = x * ((a ** t) / (y * a))
    else if (t <= 4.2d+83) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.8e-14) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if (t <= 4.2e+83) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.8e-14:
		tmp = x * (math.pow(a, t) / (y * a))
	elif t <= 4.2e+83:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.8e-14)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (t <= 4.2e+83)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.8e-14)
		tmp = x * ((a ^ t) / (y * a));
	elseif (t <= 4.2e+83)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.8e-14], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+83], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.7999999999999996e-14

   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. Step-by-step derivation

      1. associate-/l* 99.8%

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

      2. exp-diff 79.8%

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

      3. associate-/l/ 79.8%

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

      4. exp-sum 61.3%

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

      5. times-frac 61.3%

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

      6. *-commutative 61.3%

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

      7. exp-to-pow 61.3%

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

      8. *-commutative 61.3%

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

      9. exp-to-pow 61.3%

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

      10. sub-neg 61.3%

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

      11. metadata-eval 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. associate-/l* 61.5%

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

      2. exp-to-pow 61.5%

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

      3. sub-neg 61.5%

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

      4. metadata-eval 61.5%

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

   7. Simplified 61.5%

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

      1. unpow-prod-up 61.7%

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

      2. times-frac 61.7%

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

      3. unpow-1 61.7%

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

   9. Applied egg-rr 61.7%

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

       1. associate-/l/ 61.7%

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

       2. *-commutative 61.7%

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

       3. associate-*r/ 61.7%

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

   11. Simplified 61.7%

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

   12. Taylor expanded in b around 0 70.5%

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

   if -7.7999999999999996e-14 < t < 4.20000000000000005e83

   1. Initial program 96.8%

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

      1. associate-/l* 97.8%

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

      2. exp-diff 77.8%

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

      3. associate-/l/ 77.8%

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

      4. exp-sum 73.3%

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

      5. times-frac 73.3%

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

      6. *-commutative 73.3%

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

      7. exp-to-pow 73.3%

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

      8. *-commutative 73.3%

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

      9. exp-to-pow 74.1%

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

      10. sub-neg 74.1%

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

      11. metadata-eval 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in y around 0 60.9%

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

      1. associate-/l* 64.9%

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

      2. exp-to-pow 65.4%

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

      3. sub-neg 65.4%

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

      4. metadata-eval 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in t around 0 70.8%

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

   if 4.20000000000000005e83 < t

   1. Initial program 100.0%

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

      1. associate-/l* 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. exp-diff 82.4%

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

      3. associate-/l/ 82.4%

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

      4. exp-sum 66.7%

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

      5. times-frac 66.7%

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

      6. *-commutative 66.7%

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

      7. exp-to-pow 66.7%

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

      8. *-commutative 66.7%

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

      9. exp-to-pow 66.7%

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

      10. sub-neg 66.7%

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

      11. metadata-eval 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in y around 0 80.4%

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

      1. associate-/l* 80.4%

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

      2. exp-to-pow 80.4%

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

      3. sub-neg 80.4%

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

      4. metadata-eval 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in b around 0 94.2%

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

      1. remove-double-neg 94.2%

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

      2. log-rec 94.2%

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

      3. distribute-lft-neg-in 94.2%

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

      4. mul-1-neg 94.2%

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

      5. mul-1-neg 94.2%

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

      6. distribute-lft-neg-in 94.2%

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

      7. log-rec 94.2%

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

      8. remove-double-neg 94.2%

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

      9. associate-/l* 94.2%

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

   10. Simplified 94.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.5% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. associate-/l* 98.8%

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

   2. exp-diff 79.2%

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

   3. associate-/l/ 79.2%

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

   4. exp-sum 68.7%

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

   5. times-frac 68.7%

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

   6. *-commutative 68.7%

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

   7. exp-to-pow 68.7%

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

   8. *-commutative 68.7%

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

   9. exp-to-pow 69.1%

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

   10. sub-neg 69.1%

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

   11. metadata-eval 69.1%

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

3. Simplified 69.1%

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

5. Taylor expanded in y around 0 65.0%

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

   1. associate-/l* 67.0%

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

   2. exp-to-pow 67.3%

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

   3. sub-neg 67.3%

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

   4. metadata-eval 67.3%

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

7. Simplified 67.3%

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

8. Taylor expanded in t around 0 56.8%

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

9. Final simplification 56.8%

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

Alternative 10: 36.2% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{y} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot a\right) - \left(y \cdot a\right) \cdot \left(x \cdot b\right)}{\left(y \cdot a\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-157} \lor \neg \left(b \leq 5 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-197)
   (- (/ x (* y a)) (* (/ x y) (/ b a)))
   (if (<= b 7.5e-217)
     (/ (- (* x (* y a)) (* (* y a) (* x b))) (* (* y a) (* y a)))
     (if (or (<= b 2.9e-157) (not (<= b 5e+115)))
       (/ x (* a (* y b)))
       (/ (/ x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-197) {
		tmp = (x / (y * a)) - ((x / y) * (b / a));
	} else if (b <= 7.5e-217) {
		tmp = ((x * (y * a)) - ((y * a) * (x * b))) / ((y * a) * (y * a));
	} else if ((b <= 2.9e-157) || !(b <= 5e+115)) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / 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 <= (-3d-197)) then
        tmp = (x / (y * a)) - ((x / y) * (b / a))
    else if (b <= 7.5d-217) then
        tmp = ((x * (y * a)) - ((y * a) * (x * b))) / ((y * a) * (y * a))
    else if ((b <= 2.9d-157) .or. (.not. (b <= 5d+115))) then
        tmp = x / (a * (y * b))
    else
        tmp = (x / 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 <= -3e-197) {
		tmp = (x / (y * a)) - ((x / y) * (b / a));
	} else if (b <= 7.5e-217) {
		tmp = ((x * (y * a)) - ((y * a) * (x * b))) / ((y * a) * (y * a));
	} else if ((b <= 2.9e-157) || !(b <= 5e+115)) {
		tmp = x / (a * (y * b));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-197:
		tmp = (x / (y * a)) - ((x / y) * (b / a))
	elif b <= 7.5e-217:
		tmp = ((x * (y * a)) - ((y * a) * (x * b))) / ((y * a) * (y * a))
	elif (b <= 2.9e-157) or not (b <= 5e+115):
		tmp = x / (a * (y * b))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-197)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / y) * Float64(b / a)));
	elseif (b <= 7.5e-217)
		tmp = Float64(Float64(Float64(x * Float64(y * a)) - Float64(Float64(y * a) * Float64(x * b))) / Float64(Float64(y * a) * Float64(y * a)));
	elseif ((b <= 2.9e-157) || !(b <= 5e+115))
		tmp = Float64(x / Float64(a * Float64(y * b)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-197)
		tmp = (x / (y * a)) - ((x / y) * (b / a));
	elseif (b <= 7.5e-217)
		tmp = ((x * (y * a)) - ((y * a) * (x * b))) / ((y * a) * (y * a));
	elseif ((b <= 2.9e-157) || ~((b <= 5e+115)))
		tmp = x / (a * (y * b));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-197], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-217], N[(N[(N[(x * N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(y * a), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * a), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.9e-157], N[Not[LessEqual[b, 5e+115]], $MachinePrecision]], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.00000000000000026e-197

   1. Initial program 97.4%

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

      1. associate-/l* 99.4%

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

      2. exp-diff 75.2%

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

      3. associate-/l/ 75.2%

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

      4. exp-sum 67.4%

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

      5. times-frac 67.4%

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

      6. *-commutative 67.4%

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

      7. exp-to-pow 67.4%

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

      8. *-commutative 67.4%

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

      9. exp-to-pow 67.9%

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

      10. sub-neg 67.9%

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

      11. metadata-eval 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in y around 0 60.1%

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

      1. associate-/l* 63.1%

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

      2. exp-to-pow 63.5%

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

      3. sub-neg 63.5%

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

      4. metadata-eval 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in t around 0 66.8%

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

   9. Taylor expanded in b around 0 44.5%

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

       1. +-commutative 44.5%

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

       2. mul-1-neg 44.5%

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

       3. unsub-neg 44.5%

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

       4. *-commutative 44.5%

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

       5. *-commutative 44.5%

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

       6. times-frac 48.0%

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

   11. Simplified 48.0%

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

   if -3.00000000000000026e-197 < b < 7.50000000000000031e-217

   1. Initial program 96.9%

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

      1. associate-/l* 96.9%

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

      2. exp-diff 96.9%

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

      3. associate-/l/ 96.9%

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

      4. exp-sum 79.1%

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

      5. times-frac 79.1%

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

      6. *-commutative 79.1%

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

      7. exp-to-pow 79.1%

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

      8. *-commutative 79.1%

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

      9. exp-to-pow 79.7%

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

      10. sub-neg 79.7%

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

      11. metadata-eval 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in y around 0 78.2%

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

      1. associate-/l* 76.0%

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

      2. exp-to-pow 76.7%

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

      3. sub-neg 76.7%

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

      4. metadata-eval 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in t around 0 31.7%

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

   9. Taylor expanded in b around 0 27.2%

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

       1. associate-*r/ 27.2%

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

       2. frac-2neg 27.2%

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

       3. frac-add 40.0%

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

       4. neg-mul-1 40.0%

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

       5. distribute-rgt-neg-in 40.0%

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

       6. *-commutative 40.0%

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

       7. distribute-rgt-neg-in 40.0%

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

       8. *-commutative 40.0%

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

       9. *-commutative 40.0%

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

       10. *-commutative 40.0%

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

       11. distribute-rgt-neg-in 40.0%

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

   11. Applied egg-rr 40.0%

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

   if 7.50000000000000031e-217 < b < 2.89999999999999988e-157 or 5.00000000000000008e115 < 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. exp-diff 72.0%

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

      3. associate-/l/ 72.0%

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

      4. exp-sum 64.0%

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

      5. times-frac 64.0%

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

      6. *-commutative 64.0%

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

      7. exp-to-pow 64.0%

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

      8. *-commutative 64.0%

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

      9. exp-to-pow 64.0%

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

      10. sub-neg 64.0%

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

      11. metadata-eval 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in y around 0 70.1%

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

      1. associate-/l* 74.1%

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

      2. exp-to-pow 74.1%

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

      3. sub-neg 74.1%

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

      4. metadata-eval 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in t around 0 72.6%

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

   9. Taylor expanded in b around 0 51.4%

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

       1. distribute-lft-out 51.4%

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

       2. *-commutative 51.4%

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

   11. Simplified 51.4%

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

   12. Taylor expanded in b around inf 57.2%

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

       1. *-commutative 57.2%

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

   14. Simplified 57.2%

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

   if 2.89999999999999988e-157 < b < 5.00000000000000008e115

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. mul-1-neg 86.0%

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

      3. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in b around 0 67.5%

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

      1. div-exp 67.5%

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

      2. *-commutative 67.5%

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

      3. exp-to-pow 67.5%

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

      4. rem-exp-log 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in y around 0 26.3%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{y} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot a\right) - \left(y \cdot a\right) \cdot \left(x \cdot b\right)}{\left(y \cdot a\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-157} \lor \neg \left(b \leq 5 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.4% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{y} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.25e-107)
   (- (/ x (* y a)) (* (/ x y) (/ b a)))
   (if (<= b 4e+114) (/ 1.0 (* y (/ a x))) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.25e-107) {
		tmp = (x / (y * a)) - ((x / y) * (b / a));
	} else if (b <= 4e+114) {
		tmp = 1.0 / (y * (a / x));
	} 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 <= (-2.25d-107)) then
        tmp = (x / (y * a)) - ((x / y) * (b / a))
    else if (b <= 4d+114) then
        tmp = 1.0d0 / (y * (a / x))
    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 <= -2.25e-107) {
		tmp = (x / (y * a)) - ((x / y) * (b / a));
	} else if (b <= 4e+114) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.25e-107:
		tmp = (x / (y * a)) - ((x / y) * (b / a))
	elif b <= 4e+114:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.25e-107)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / y) * Float64(b / a)));
	elseif (b <= 4e+114)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	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 <= -2.25e-107)
		tmp = (x / (y * a)) - ((x / y) * (b / a));
	elseif (b <= 4e+114)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.25e-107], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+114], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.25000000000000008e-107

   1. Initial program 97.0%

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

      1. associate-/l* 99.4%

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

      2. exp-diff 71.0%

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

      3. associate-/l/ 71.0%

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

      4. exp-sum 63.1%

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

      5. times-frac 63.1%

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

      6. *-commutative 63.1%

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

      7. exp-to-pow 63.1%

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

      8. *-commutative 63.1%

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

      9. exp-to-pow 63.6%

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

      10. sub-neg 63.6%

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

      11. metadata-eval 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in y around 0 61.1%

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

      1. associate-/l* 64.6%

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

      2. exp-to-pow 65.0%

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

      3. sub-neg 65.0%

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

      4. metadata-eval 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in t around 0 72.1%

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

   9. Taylor expanded in b around 0 46.1%

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

       1. +-commutative 46.1%

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

       2. mul-1-neg 46.1%

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

       3. unsub-neg 46.1%

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

       4. *-commutative 46.1%

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

       5. *-commutative 46.1%

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

       6. times-frac 50.2%

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

   11. Simplified 50.2%

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

   if -2.25000000000000008e-107 < b < 4e114

   1. Initial program 98.6%

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

      1. associate-/l* 98.0%

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

      2. exp-diff 89.5%

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

      3. associate-/l/ 89.5%

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

      4. exp-sum 75.7%

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

      5. times-frac 75.7%

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

      6. *-commutative 75.7%

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

      7. exp-to-pow 75.7%

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

      8. *-commutative 75.7%

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

      9. exp-to-pow 76.1%

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

      10. sub-neg 76.1%

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

      11. metadata-eval 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in b around 0 75.0%

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

      1. associate-/l* 74.3%

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

      2. *-commutative 74.3%

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

      3. exp-to-pow 74.7%

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

      4. sub-neg 74.7%

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

      5. metadata-eval 74.7%

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

      6. associate-/l* 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in t around 0 54.6%

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

      1. associate-/r* 56.2%

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

   10. Simplified 56.2%

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

   11. Taylor expanded in y around 0 23.3%

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

       1. div-inv 23.4%

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

       2. *-commutative 23.4%

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

       3. clear-num 23.7%

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

       4. associate-/l* 29.6%

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

   13. Applied egg-rr 29.6%

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

   if 4e114 < 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. exp-diff 63.2%

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

      3. associate-/l/ 63.2%

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

      4. exp-sum 57.9%

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

      5. times-frac 57.9%

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

      6. *-commutative 57.9%

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

      7. exp-to-pow 57.9%

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

      8. *-commutative 57.9%

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

      9. exp-to-pow 57.9%

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

      10. sub-neg 57.9%

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

      11. metadata-eval 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. associate-/l* 71.1%

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

      2. exp-to-pow 71.1%

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

      3. sub-neg 71.1%

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

      4. metadata-eval 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around 0 89.6%

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

   9. Taylor expanded in b around 0 61.8%

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

       1. distribute-lft-out 61.8%

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

       2. *-commutative 61.8%

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

   11. Simplified 61.8%

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

   12. Taylor expanded in b around inf 61.8%

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

       1. *-commutative 61.8%

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

   14. Simplified 61.8%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{y} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.6e+94)
   (* x (/ b (* y (- a))))
   (if (<= b 4.3e+114) (* (/ x y) (/ 1.0 a)) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+94) {
		tmp = x * (b / (y * -a));
	} else if (b <= 4.3e+114) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.6d+94)) then
        tmp = x * (b / (y * -a))
    else if (b <= 4.3d+114) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+94) {
		tmp = x * (b / (y * -a));
	} else if (b <= 4.3e+114) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.6e+94:
		tmp = x * (b / (y * -a))
	elif b <= 4.3e+114:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.6e+94)
		tmp = Float64(x * Float64(b / Float64(y * Float64(-a))));
	elseif (b <= 4.3e+114)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.6e+94)
		tmp = x * (b / (y * -a));
	elseif (b <= 4.3e+114)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.6e+94], N[(x * N[(b / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+114], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5999999999999999e94

   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. exp-diff 60.9%

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

      3. associate-/l/ 60.9%

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

      4. exp-sum 50.0%

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

      5. times-frac 50.0%

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

      6. *-commutative 50.0%

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

      7. exp-to-pow 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y around 0 58.9%

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

      1. associate-/l* 61.1%

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

      2. exp-to-pow 61.1%

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

      3. sub-neg 61.1%

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

      4. metadata-eval 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in t around 0 87.2%

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

   9. Taylor expanded in b around 0 47.4%

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

   10. Taylor expanded in b around inf 47.4%

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

       1. *-commutative 47.4%

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

       2. *-commutative 47.4%

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

       3. associate-*r/ 53.7%

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

       4. neg-mul-1 53.7%

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

       5. distribute-rgt-neg-in 53.7%

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

       6. distribute-frac-neg 53.7%

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

   12. Simplified 53.7%

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

   if -2.5999999999999999e94 < b < 4.3000000000000001e114

   1. Initial program 97.4%

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

      1. associate-/l* 98.2%

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

      2. exp-diff 87.7%

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

      3. associate-/l/ 87.7%

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

      4. exp-sum 76.1%

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

      5. times-frac 76.1%

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

      6. *-commutative 76.1%

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

      7. exp-to-pow 76.1%

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

      8. *-commutative 76.1%

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

      9. exp-to-pow 76.7%

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

      10. sub-neg 76.7%

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

      11. metadata-eval 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around 0 66.4%

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

      1. associate-/l* 67.7%

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

      2. exp-to-pow 68.2%

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

      3. sub-neg 68.2%

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

      4. metadata-eval 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in t around 0 41.4%

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

   9. Taylor expanded in b around 0 28.0%

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

       1. *-commutative 28.0%

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

   11. Simplified 28.0%

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

       1. *-rgt-identity 28.0%

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

       2. times-frac 32.6%

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

   13. Applied egg-rr 32.6%

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

   if 4.3000000000000001e114 < 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. exp-diff 63.2%

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

      3. associate-/l/ 63.2%

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

      4. exp-sum 57.9%

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

      5. times-frac 57.9%

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

      6. *-commutative 57.9%

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

      7. exp-to-pow 57.9%

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

      8. *-commutative 57.9%

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

      9. exp-to-pow 57.9%

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

      10. sub-neg 57.9%

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

      11. metadata-eval 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. associate-/l* 71.1%

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

      2. exp-to-pow 71.1%

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

      3. sub-neg 71.1%

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

      4. metadata-eval 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around 0 89.6%

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

   9. Taylor expanded in b around 0 61.8%

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

       1. distribute-lft-out 61.8%

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

       2. *-commutative 61.8%

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

   11. Simplified 61.8%

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

   12. Taylor expanded in b around inf 61.8%

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

       1. *-commutative 61.8%

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

   14. Simplified 61.8%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-y}}{a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e+14)
   (/ (* x (/ b (- y))) a)
   (if (<= b 5.2e+114) (/ 1.0 (* y (/ a x))) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e+14) {
		tmp = (x * (b / -y)) / a;
	} else if (b <= 5.2e+114) {
		tmp = 1.0 / (y * (a / x));
	} 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 <= (-2.1d+14)) then
        tmp = (x * (b / -y)) / a
    else if (b <= 5.2d+114) then
        tmp = 1.0d0 / (y * (a / x))
    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 <= -2.1e+14) {
		tmp = (x * (b / -y)) / a;
	} else if (b <= 5.2e+114) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.1e+14:
		tmp = (x * (b / -y)) / a
	elif b <= 5.2e+114:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e+14)
		tmp = Float64(Float64(x * Float64(b / Float64(-y))) / a);
	elseif (b <= 5.2e+114)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	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 <= -2.1e+14)
		tmp = (x * (b / -y)) / a;
	elseif (b <= 5.2e+114)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e+14], N[(N[(x * N[(b / (-y)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 5.2e+114], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1e14

   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. exp-diff 60.7%

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

      3. associate-/l/ 60.7%

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

      4. exp-sum 52.5%

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

      5. times-frac 52.5%

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

      6. *-commutative 52.5%

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

      7. exp-to-pow 52.5%

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

      8. *-commutative 52.5%

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

      9. exp-to-pow 52.5%

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

      10. sub-neg 52.5%

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

      11. metadata-eval 52.5%

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

   3. Simplified 52.5%

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

   5. Taylor expanded in y around 0 59.2%

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

      1. associate-/l* 60.8%

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

      2. exp-to-pow 60.8%

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

      3. sub-neg 60.8%

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

      4. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in t around 0 80.6%

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

   9. Taylor expanded in b around 0 44.6%

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

   10. Taylor expanded in b around inf 44.6%

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

       1. mul-1-neg 44.6%

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

       2. times-frac 53.6%

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

       3. distribute-rgt-neg-out 53.6%

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

       4. associate-*l/ 49.1%

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

       5. distribute-rgt-neg-in 49.1%

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

       6. associate-/l* 50.8%

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

       7. *-commutative 50.8%

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

       8. associate-/l* 50.8%

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

       9. distribute-rgt-neg-in 50.8%

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

   12. Simplified 50.8%

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

   if -2.1e14 < b < 5.2000000000000001e114

   1. Initial program 97.2%

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

      1. associate-/l* 98.0%

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

      2. exp-diff 90.4%

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

      3. associate-/l/ 90.4%

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

      4. exp-sum 77.6%

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

      5. times-frac 77.6%

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

      6. *-commutative 77.6%

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

      7. exp-to-pow 77.6%

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

      8. *-commutative 77.6%

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

      9. exp-to-pow 78.3%

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

      10. sub-neg 78.3%

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

      11. metadata-eval 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in b around 0 76.4%

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

      1. associate-/l* 77.1%

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

      2. *-commutative 77.1%

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

      3. exp-to-pow 77.8%

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

      4. sub-neg 77.8%

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

      5. metadata-eval 77.8%

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

      6. associate-/l* 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around 0 57.4%

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

      1. associate-/r* 58.7%

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

   10. Simplified 58.7%

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

   11. Taylor expanded in y around 0 27.8%

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

       1. div-inv 27.8%

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

       2. *-commutative 27.8%

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

       3. clear-num 27.9%

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

       4. associate-/l* 32.2%

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

   13. Applied egg-rr 32.2%

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

   if 5.2000000000000001e114 < 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. exp-diff 63.2%

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

      3. associate-/l/ 63.2%

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

      4. exp-sum 57.9%

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

      5. times-frac 57.9%

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

      6. *-commutative 57.9%

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

      7. exp-to-pow 57.9%

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

      8. *-commutative 57.9%

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

      9. exp-to-pow 57.9%

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

      10. sub-neg 57.9%

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

      11. metadata-eval 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. associate-/l* 71.1%

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

      2. exp-to-pow 71.1%

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

      3. sub-neg 71.1%

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

      4. metadata-eval 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around 0 89.6%

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

   9. Taylor expanded in b around 0 61.8%

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

       1. distribute-lft-out 61.8%

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

       2. *-commutative 61.8%

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

   11. Simplified 61.8%

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

   12. Taylor expanded in b around inf 61.8%

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

       1. *-commutative 61.8%

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

   14. Simplified 61.8%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-y}}{a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.3% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(b + -1\right)}{-y}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e+97)
   (/ (* (/ x a) (+ b -1.0)) (- y))
   (if (<= b 5.4e+116) (* (/ x y) (/ 1.0 a)) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+97) {
		tmp = ((x / a) * (b + -1.0)) / -y;
	} else if (b <= 5.4e+116) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4d+97)) then
        tmp = ((x / a) * (b + (-1.0d0))) / -y
    else if (b <= 5.4d+116) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+97) {
		tmp = ((x / a) * (b + -1.0)) / -y;
	} else if (b <= 5.4e+116) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e+97:
		tmp = ((x / a) * (b + -1.0)) / -y
	elif b <= 5.4e+116:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e+97)
		tmp = Float64(Float64(Float64(x / a) * Float64(b + -1.0)) / Float64(-y));
	elseif (b <= 5.4e+116)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4e+97)
		tmp = ((x / a) * (b + -1.0)) / -y;
	elseif (b <= 5.4e+116)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e+97], N[(N[(N[(x / a), $MachinePrecision] * N[(b + -1.0), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, 5.4e+116], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.0000000000000003e97

   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. exp-diff 60.9%

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

      3. associate-/l/ 60.9%

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

      4. exp-sum 50.0%

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

      5. times-frac 50.0%

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

      6. *-commutative 50.0%

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

      7. exp-to-pow 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y around 0 58.9%

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

      1. associate-/l* 61.1%

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

      2. exp-to-pow 61.1%

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

      3. sub-neg 61.1%

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

      4. metadata-eval 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in t around 0 87.2%

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

   9. Taylor expanded in b around 0 47.4%

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

   10. Taylor expanded in y around 0 59.8%

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

       1. remove-double-neg 59.8%

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

       2. neg-mul-1 59.8%

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

       3. *-lft-identity 59.8%

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

       4. times-frac 59.8%

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

       5. metadata-eval 59.8%

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

       6. distribute-neg-frac 59.8%

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

       7. distribute-lft-in 59.8%

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

       8. +-commutative 59.8%

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

       9. neg-mul-1 59.8%

          \[\leadsto \frac{-1 \cdot \left(\color{blue}{-1 \cdot \frac{x}{a}} + \frac{b \cdot x}{a}\right)}{y} \]

       10. associate-*r/ 59.8%

           \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{a} + \frac{b \cdot x}{a}}{y}} \]

       11. mul-1-neg 59.8%

           \[\leadsto \color{blue}{-\frac{-1 \cdot \frac{x}{a} + \frac{b \cdot x}{a}}{y}} \]

       12. distribute-neg-frac2 59.8%

           \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{a} + \frac{b \cdot x}{a}}{-y}} \]

       13. neg-mul-1 59.8%

           \[\leadsto \frac{\color{blue}{\left(-\frac{x}{a}\right)} + \frac{b \cdot x}{a}}{-y} \]

       14. +-commutative 59.8%

           \[\leadsto \frac{\color{blue}{\frac{b \cdot x}{a} + \left(-\frac{x}{a}\right)}}{-y} \]

       15. associate-/l* 57.7%

           \[\leadsto \frac{\color{blue}{b \cdot \frac{x}{a}} + \left(-\frac{x}{a}\right)}{-y} \]

       16. neg-mul-1 57.7%

           \[\leadsto \frac{b \cdot \frac{x}{a} + \color{blue}{-1 \cdot \frac{x}{a}}}{-y} \]

       17. distribute-rgt-out 57.7%

           \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(b + -1\right)}}{-y} \]

   12. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot \left(b + -1\right)}{-y}} \]

   if -4.0000000000000003e97 < b < 5.3999999999999999e116

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 87.7%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 87.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 76.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 76.1%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 76.1%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 76.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 76.1%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 76.7%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 76.7%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 76.7%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 68.2%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 68.2%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 68.2%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 68.2%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 41.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 28.0%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 28.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 28.0%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-rgt-identity 28.0%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{y \cdot a} \]

       2. times-frac 32.6%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   13. Applied egg-rr 32.6%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   if 5.3999999999999999e116 < 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. exp-diff 63.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 63.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 57.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 57.9%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 57.9%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 57.9%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 57.9%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 57.9%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 71.1%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 71.1%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 89.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 61.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 61.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 61.8%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 61.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 61.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(b + -1\right)}{-y}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+117}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2e-256)
   (/ (- (/ x y) (/ (* x b) y)) a)
   (if (<= b 5.2e+117) (/ (/ 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 <= 2e-256) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 5.2e+117) {
		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 <= 2d-256) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else if (b <= 5.2d+117) 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 <= 2e-256) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 5.2e+117) {
		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 <= 2e-256:
		tmp = ((x / y) - ((x * b) / y)) / a
	elif b <= 5.2e+117:
		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 <= 2e-256)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	elseif (b <= 5.2e+117)
		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 <= 2e-256)
		tmp = ((x / y) - ((x * b) / y)) / a;
	elseif (b <= 5.2e+117)
		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, 2e-256], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 5.2e+117], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 1.99999999999999995e-256

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 80.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 80.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 70.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 70.0%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 70.0%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 70.0%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 70.0%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 70.6%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 70.6%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 70.6%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 67.6%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 67.6%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 67.6%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 56.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in a around 0 44.8%

       \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}}{a}} \]

   if 1.99999999999999995e-256 < b < 5.1999999999999999e117

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 77.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 77.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 77.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 77.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 77.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 64.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. div-exp 64.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 64.8%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 64.8%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 65.1%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   8. Simplified 65.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   9. Taylor expanded in y around 0 27.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 5.1999999999999999e117 < 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. exp-diff 63.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 63.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 57.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 57.9%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 57.9%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 57.9%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 57.9%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 57.9%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 71.1%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 71.1%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 89.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 61.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 61.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 61.8%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 61.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 61.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2 \cdot 10^{-256}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+117}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.6e-23) (/ (/ x a) y) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e-23) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.6d-23)) then
        tmp = (x / a) / y
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e-23) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.6e-23:
		tmp = (x / a) / y
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.6e-23)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.6e-23)
		tmp = (x / a) / y;
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.6e-23], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.60000000000000004e-23

   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 t around 0 80.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 80.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 80.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 80.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 80.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 71.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. div-exp 71.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 71.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 71.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 71.5%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   8. Simplified 71.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   9. Taylor expanded in y around 0 35.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -8.60000000000000004e-23 < t

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 78.8%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 78.8%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 71.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 71.2%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 71.2%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 71.2%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 71.2%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 71.7%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 71.7%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 71.7%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 68.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 69.2%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 69.2%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 69.2%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 58.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 27.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 27.6%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 27.6%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-rgt-identity 27.6%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{y \cdot a} \]

       2. times-frac 30.6%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   13. Applied egg-rr 30.6%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.5e-23) (/ 1.0 (* y (/ a x))) (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e-23) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.5d-23)) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.5e-23) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.5e-23:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.5e-23)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.5e-23)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.5e-23], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.4999999999999996e-23

   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. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 80.4%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 62.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 62.3%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 62.3%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 62.3%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 62.3%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 62.3%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 62.3%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 62.3%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 62.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 68.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(e^{\log a \cdot \left(t - 1\right)} \cdot {z}^{y}\right)}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 68.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)} \cdot {z}^{y}}{y}} \]

      2. *-commutative 68.0%

         \[\leadsto x \cdot \frac{\color{blue}{{z}^{y} \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]

      3. exp-to-pow 68.0%

         \[\leadsto x \cdot \frac{{z}^{y} \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

      4. sub-neg 68.0%

         \[\leadsto x \cdot \frac{{z}^{y} \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

      5. metadata-eval 68.0%

         \[\leadsto x \cdot \frac{{z}^{y} \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

      6. associate-/l* 68.0%

         \[\leadsto x \cdot \color{blue}{\left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y}\right)} \]

   7. Simplified 68.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{y}\right)} \]

   8. Taylor expanded in t around 0 59.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \color{blue}{\frac{1}{a \cdot y}}\right) \]
   9. Step-by-step derivation

      1. associate-/r* 62.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

   10. Simplified 62.1%

       \[\leadsto x \cdot \left({z}^{y} \cdot \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

   11. Taylor expanded in y around 0 24.8%

       \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   12. Step-by-step derivation

       1. div-inv 24.8%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

       2. *-commutative 24.8%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

       3. clear-num 24.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       4. associate-/l* 36.5%

          \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{a}{x}}} \]

   13. Applied egg-rr 36.5%

       \[\leadsto \color{blue}{\frac{1}{y \cdot \frac{a}{x}}} \]

   if -8.4999999999999996e-23 < t

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 78.8%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 78.8%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 71.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 71.2%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 71.2%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 71.2%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 71.2%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 71.7%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 71.7%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 71.7%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 68.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 69.2%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 69.2%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 69.2%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 58.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 27.6%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 27.6%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 27.6%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-rgt-identity 27.6%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{y \cdot a} \]

       2. times-frac 30.6%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   13. Applied egg-rr 30.6%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.2% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.3e+115) (* (/ x y) (/ 1.0 a)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.3e+115) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.3d+115) then
        tmp = (x / y) * (1.0d0 / a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.3e+115) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.3e+115:
		tmp = (x / y) * (1.0 / a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.3e+115)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.3e+115)
		tmp = (x / y) * (1.0 / a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.3e+115], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.3e115

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. exp-diff 82.0%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 82.0%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 70.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 70.6%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 70.6%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 70.6%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 70.6%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 71.0%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 71.0%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 71.0%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 66.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 66.7%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 66.7%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 66.7%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 51.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 28.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 28.5%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   11. Simplified 28.5%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]
   12. Step-by-step derivation

       1. *-rgt-identity 28.5%

          \[\leadsto \frac{\color{blue}{x \cdot 1}}{y \cdot a} \]

       2. times-frac 31.3%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   13. Applied egg-rr 31.3%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{a}} \]

   if 1.3e115 < 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. exp-diff 63.2%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

      3. associate-/l/ 63.2%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

      4. exp-sum 57.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

      5. times-frac 57.9%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

      6. *-commutative 57.9%

         \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      7. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

      8. *-commutative 57.9%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

      9. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

      10. sub-neg 57.9%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

      11. metadata-eval 57.9%

          \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

   3. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

      2. exp-to-pow 71.1%

         \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      3. sub-neg 71.1%

         \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      4. metadata-eval 71.1%

         \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   7. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 89.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 61.8%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-lft-out 61.8%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 61.8%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   11. Simplified 61.8%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   12. Taylor expanded in b around inf 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 61.8%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 61.8%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.2% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e-22) (/ (/ x a) y) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-22) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d-22)) then
        tmp = (x / a) / y
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-22) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e-22:
		tmp = (x / a) / y
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e-22)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e-22)
		tmp = (x / a) / y;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e-22], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e-22

   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 t around 0 80.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 80.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 80.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 80.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 80.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 71.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. div-exp 71.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 71.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 71.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 71.5%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   8. Simplified 71.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   9. Taylor expanded in y around 0 35.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -1e-22 < t

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 83.3%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 83.3%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 83.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 60.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   7. Step-by-step derivation

      1. div-exp 60.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 60.1%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 60.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 60.7%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   8. Simplified 60.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   9. Taylor expanded in x around 0 51.6%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   10. Step-by-step derivation

       1. *-commutative 51.6%

          \[\leadsto \frac{\color{blue}{{z}^{y} \cdot x}}{a \cdot y} \]

       2. times-frac 57.9%

          \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y}} \]

   11. Simplified 57.9%

       \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y}} \]

   12. Taylor expanded in y around 0 27.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. associate-/l/ 30.6%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]

   14. Simplified 30.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.0% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.8%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. exp-diff 79.2%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \]

   3. associate-/l/ 79.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y \cdot e^{b}}} \]

   4. exp-sum 68.7%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{y \cdot e^{b}} \]

   5. times-frac 68.7%

      \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right)} \]

   6. *-commutative 68.7%

      \[\leadsto x \cdot \left(\frac{e^{\color{blue}{\log z \cdot y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

   7. exp-to-pow 68.7%

      \[\leadsto x \cdot \left(\frac{\color{blue}{{z}^{y}}}{y} \cdot \frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}\right) \]

   8. *-commutative 68.7%

      \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}\right) \]

   9. exp-to-pow 69.1%

      \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}\right) \]

   10. sub-neg 69.1%

       \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}\right) \]

   11. metadata-eval 69.1%

       \[\leadsto x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}\right) \]

3. Simplified 69.1%

   \[\leadsto \color{blue}{x \cdot \left(\frac{{z}^{y}}{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 65.0%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. associate-/l* 67.0%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]

   2. exp-to-pow 67.3%

      \[\leadsto x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   3. sub-neg 67.3%

      \[\leadsto x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   4. metadata-eval 67.3%

      \[\leadsto x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

7. Simplified 67.3%

   \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

8. Taylor expanded in t around 0 56.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 26.8%

   \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
10. Step-by-step derivation

    1. *-commutative 26.8%

       \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

11. Simplified 26.8%

    \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

12. Final simplification 26.8%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Alternative 21: 31.6% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 82.6%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
4. Step-by-step derivation

   1. +-commutative 82.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

   2. mul-1-neg 82.6%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   3. unsub-neg 82.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

5. Simplified 82.6%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

6. Taylor expanded in b around 0 63.3%

   \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
7. Step-by-step derivation

   1. div-exp 63.3%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

   2. *-commutative 63.3%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

   3. exp-to-pow 63.3%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

   4. rem-exp-log 63.7%

      \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

8. Simplified 63.7%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

9. Taylor expanded in y around 0 28.5%

   \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

10. Final simplification 28.5%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
11. 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 2024039 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))