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

Percentage Accurate: 98.4% → 98.4%

Time: 29.7s

Alternatives: 22

Speedup: 1.0×

• 20.9% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

2. Final simplification 98.6%

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

Alternative 2: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-9} \lor \neg \left(y \leq 2.35 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.5e-9) (not (<= y 2.35e-37)))
   (/ (* 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 ((y <= -3.5e-9) || !(y <= 2.35e-37)) {
		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 ((y <= (-3.5d-9)) .or. (.not. (y <= 2.35d-37))) 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 ((y <= -3.5e-9) || !(y <= 2.35e-37)) {
		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 (y <= -3.5e-9) or not (y <= 2.35e-37):
		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 ((y <= -3.5e-9) || !(y <= 2.35e-37))
		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 ((y <= -3.5e-9) || ~((y <= 2.35e-37)))
		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[Or[LessEqual[y, -3.5e-9], N[Not[LessEqual[y, 2.35e-37]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(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 < -3.4999999999999999e-9 or 2.3500000000000001e-37 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 91.7%

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

      1. mul-1-neg 91.7%

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

   4. Simplified 91.7%

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

   if -3.4999999999999999e-9 < y < 2.3500000000000001e-37

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 97.3%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-9} \lor \neg \left(y \leq 2.35 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+37} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+37) (not (<= (+ t -1.0) -0.5)))
   (/ (* x (/ (pow a t) a)) y)
   (* (/ (pow z y) a) (/ x (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+37) || !((t + -1.0) <= -0.5)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = (pow(z, y) / a) * (x / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+37)) .or. (.not. ((t + (-1.0d0)) <= (-0.5d0)))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = ((z ** y) / a) * (x / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+37) || !((t + -1.0) <= -0.5)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = (Math.pow(z, y) / a) * (x / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+37) or not ((t + -1.0) <= -0.5):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = (math.pow(z, y) / a) * (x / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+37) || !(Float64(t + -1.0) <= -0.5))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+37) || ~(((t + -1.0) <= -0.5)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = ((z ^ y) / a) * (x / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+37], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -9.99999999999999954e36 or -0.5 < (-.f64 t 1)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

   3. Taylor expanded in b around 0 81.9%

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

      1. expm1-log1p-u 81.9%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)}\right)\right)} \cdot x}{y} \]

      2. expm1-udef 81.9%

         \[\leadsto \frac{\color{blue}{\left(e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)}\right)} - 1\right)} \cdot x}{y} \]

      3. pow-sub 81.9%

         \[\leadsto \frac{\left(e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1\right) \cdot x}{y} \]

      4. pow1 81.9%

         \[\leadsto \frac{\left(e^{\mathsf{log1p}\left(\frac{{a}^{t}}{\color{blue}{a}}\right)} - 1\right) \cdot x}{y} \]

   5. Applied egg-rr 81.9%

      \[\leadsto \frac{\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)} - 1\right)} \cdot x}{y} \]
   6. Step-by-step derivation

      1. expm1-def 81.9%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)\right)} \cdot x}{y} \]

      2. expm1-log1p 81.9%

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

   7. Simplified 81.9%

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

   if -9.99999999999999954e36 < (-.f64 t 1) < -0.5

   1. Initial program 97.5%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

      3. +-commutative 91.9%

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

      4. associate--l+ 91.9%

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

      5. exp-sum 91.2%

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

      6. *-commutative 91.2%

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

      7. exp-to-pow 92.1%

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

      8. sub-neg 92.1%

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

      9. metadata-eval 92.1%

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

      10. exp-diff 81.6%

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

      11. *-commutative 81.6%

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

      12. exp-to-pow 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. times-frac 85.3%

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

   6. Simplified 85.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+37} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \]

Alternative 4: 88.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-8} \lor \neg \left(y \leq 8.6 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-8) (not (<= y 8.6e+82)))
   (/ (* 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 <= -1.25e-8) || !(y <= 8.6e+82)) {
		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 <= (-1.25d-8)) .or. (.not. (y <= 8.6d+82))) 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 <= -1.25e-8) || !(y <= 8.6e+82)) {
		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 <= -1.25e-8) or not (y <= 8.6e+82):
		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 <= -1.25e-8) || !(y <= 8.6e+82))
		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 <= -1.25e-8) || ~((y <= 8.6e+82)))
		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, -1.25e-8], N[Not[LessEqual[y, 8.6e+82]], $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 < -1.2499999999999999e-8 or 8.60000000000000029e82 < y

   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. Taylor expanded in t around 0 92.9%

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

      1. mul-1-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in b around 0 86.0%

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

      1. div-exp 86.0%

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

      2. *-commutative 86.0%

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

      3. exp-to-pow 86.0%

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

      4. rem-exp-log 86.2%

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

   7. Simplified 86.2%

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

   if -1.2499999999999999e-8 < y < 8.60000000000000029e82

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 94.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-8} \lor \neg \left(y \leq 8.6 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 76.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+19} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+19) (not (<= (+ t -1.0) -0.5)))
   (/ (* x (/ (pow a t) a)) y)
   (/ (* x (/ (pow z y) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+19) || !((t + -1.0) <= -0.5)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = (x * (pow(z, y) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+19)) .or. (.not. ((t + (-1.0d0)) <= (-0.5d0)))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = (x * ((z ** y) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+19) || !((t + -1.0) <= -0.5)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+19) or not ((t + -1.0) <= -0.5):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = (x * (math.pow(z, y) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+19) || !(Float64(t + -1.0) <= -0.5))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+19) || ~(((t + -1.0) <= -0.5)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = (x * ((z ^ y) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+19], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -1e19 or -0.5 < (-.f64 t 1)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.2%

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

   3. Taylor expanded in b around 0 82.3%

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

      1. expm1-log1p-u 82.3%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)}\right)\right)} \cdot x}{y} \]

      2. expm1-udef 82.3%

         \[\leadsto \frac{\color{blue}{\left(e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)}\right)} - 1\right)} \cdot x}{y} \]

      3. pow-sub 82.3%

         \[\leadsto \frac{\left(e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1\right) \cdot x}{y} \]

      4. pow1 82.3%

         \[\leadsto \frac{\left(e^{\mathsf{log1p}\left(\frac{{a}^{t}}{\color{blue}{a}}\right)} - 1\right) \cdot x}{y} \]

   5. Applied egg-rr 82.3%

      \[\leadsto \frac{\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)} - 1\right)} \cdot x}{y} \]
   6. Step-by-step derivation

      1. expm1-def 82.3%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)\right)} \cdot x}{y} \]

      2. expm1-log1p 82.3%

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

   7. Simplified 82.3%

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

   if -1e19 < (-.f64 t 1) < -0.5

   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. Taylor expanded in t around 0 97.0%

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

      1. mul-1-neg 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in b around 0 77.1%

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

      1. div-exp 77.1%

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

      2. *-commutative 77.1%

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

      3. exp-to-pow 77.1%

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

      4. rem-exp-log 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+19} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 6: 76.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+19} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+19) (not (<= (+ t -1.0) -0.5)))
   (/ (* x (/ (pow a t) a)) y)
   (/ (/ (* x (pow z y)) a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+19) || !((t + -1.0) <= -0.5)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = ((x * pow(z, y)) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+19)) .or. (.not. ((t + (-1.0d0)) <= (-0.5d0)))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = ((x * (z ** y)) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+19) || !((t + -1.0) <= -0.5)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+19) or not ((t + -1.0) <= -0.5):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = ((x * math.pow(z, y)) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+19) || !(Float64(t + -1.0) <= -0.5))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+19) || ~(((t + -1.0) <= -0.5)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = ((x * (z ^ y)) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+19], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -1e19 or -0.5 < (-.f64 t 1)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.2%

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

   3. Taylor expanded in b around 0 82.3%

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

      1. expm1-log1p-u 82.3%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)}\right)\right)} \cdot x}{y} \]

      2. expm1-udef 82.3%

         \[\leadsto \frac{\color{blue}{\left(e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)}\right)} - 1\right)} \cdot x}{y} \]

      3. pow-sub 82.3%

         \[\leadsto \frac{\left(e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1\right) \cdot x}{y} \]

      4. pow1 82.3%

         \[\leadsto \frac{\left(e^{\mathsf{log1p}\left(\frac{{a}^{t}}{\color{blue}{a}}\right)} - 1\right) \cdot x}{y} \]

   5. Applied egg-rr 82.3%

      \[\leadsto \frac{\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)} - 1\right)} \cdot x}{y} \]
   6. Step-by-step derivation

      1. expm1-def 82.3%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)\right)} \cdot x}{y} \]

      2. expm1-log1p 82.3%

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

   7. Simplified 82.3%

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

   if -1e19 < (-.f64 t 1) < -0.5

   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. Taylor expanded in t around 0 97.0%

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

      1. mul-1-neg 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in b around 0 77.1%

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

      1. div-exp 77.1%

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

      2. *-commutative 77.1%

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

      3. exp-to-pow 77.1%

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

      4. rem-exp-log 78.0%

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

   7. Simplified 78.0%

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

      1. associate-*r/ 78.0%

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

   9. Applied egg-rr 78.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+19} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 7: 76.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-8} \lor \neg \left(y \leq 10200\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-8) (not (<= y 10200.0)))
   (/ (* x (/ (pow z y) a)) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e-8) || !(y <= 10200.0)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.25d-8)) .or. (.not. (y <= 10200.0d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e-8) || !(y <= 10200.0)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e-8) or not (y <= 10200.0):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e-8) || !(y <= 10200.0))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e-8) || ~((y <= 10200.0)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e-8], N[Not[LessEqual[y, 10200.0]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e-8 or 10200 < y

   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. Taylor expanded in t around 0 91.4%

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

      1. mul-1-neg 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in b around 0 84.6%

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

      1. div-exp 84.6%

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

      2. *-commutative 84.6%

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

      3. exp-to-pow 84.6%

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

      4. rem-exp-log 84.7%

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

   7. Simplified 84.7%

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

   if -1.2499999999999999e-8 < y < 10200

   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/ 87.2%

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

      2. *-commutative 87.2%

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

      3. +-commutative 87.2%

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

      4. associate--l+ 87.2%

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

      5. exp-sum 75.4%

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

      6. *-commutative 75.4%

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

      7. exp-to-pow 76.3%

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

      8. sub-neg 76.3%

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

      9. metadata-eval 76.3%

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

      10. exp-diff 75.5%

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

      11. *-commutative 75.5%

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

      12. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around 0 67.0%

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

   5. Taylor expanded in y around 0 67.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-8} \lor \neg \left(y \leq 10200\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 57.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x - a \cdot \frac{b}{\frac{a}{x}}\right)}{y \cdot \left(y \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 3.1e+237)
   (/ x (* a (* y (exp b))))
   (/ (* y (- x (* a (/ b (/ a x))))) (* y (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.1e+237) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (y * (x - (a * (b / (a / x))))) / (y * (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 (y <= 3.1d+237) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (y * (x - (a * (b / (a / x))))) / (y * (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 (y <= 3.1e+237) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (y * (x - (a * (b / (a / x))))) / (y * (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.1e+237:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (y * (x - (a * (b / (a / x))))) / (y * (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.1e+237)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(y * Float64(x - Float64(a * Float64(b / Float64(a / x))))) / Float64(y * Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.1e+237)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (y * (x - (a * (b / (a / x))))) / (y * (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.1e+237], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x - N[(a * N[(b / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.09999999999999991e237

   1. Initial program 98.5%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

      3. +-commutative 88.1%

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

      4. associate--l+ 88.1%

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

      5. exp-sum 75.5%

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

      6. *-commutative 75.5%

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

      7. exp-to-pow 76.1%

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

      8. sub-neg 76.1%

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

      9. metadata-eval 76.1%

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

      10. exp-diff 67.7%

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

      11. *-commutative 67.7%

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

      12. exp-to-pow 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around 0 66.2%

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

   5. Taylor expanded in y around 0 59.9%

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

   if 3.09999999999999991e237 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. +-commutative 94.1%

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

      4. associate--l+ 94.1%

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

      5. exp-sum 64.7%

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

      6. *-commutative 64.7%

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

      7. exp-to-pow 64.7%

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

      8. sub-neg 64.7%

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

      9. metadata-eval 64.7%

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

      10. exp-diff 52.9%

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

      11. *-commutative 52.9%

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

      12. exp-to-pow 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in t around 0 70.7%

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

   5. Taylor expanded in y around 0 15.4%

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

   6. Taylor expanded in b around 0 15.5%

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

      1. +-commutative 15.5%

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

      2. mul-1-neg 15.5%

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

      3. unsub-neg 15.5%

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

      4. times-frac 15.4%

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

   8. Simplified 15.4%

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

      1. associate-*r/ 21.0%

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

      2. frac-sub 47.2%

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

   10. Applied egg-rr 47.2%

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

       1. *-commutative 47.2%

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

       2. associate-*l* 53.1%

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

       3. distribute-lft-out-- 53.1%

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

       4. associate-*l/ 53.1%

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

       5. associate-/l* 53.1%

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

       6. *-commutative 53.1%

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

   12. Simplified 53.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x - a \cdot \frac{b}{\frac{a}{x}}\right)}{y \cdot \left(y \cdot a\right)}\\ \end{array} \]

Alternative 9: 40.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot b\\ \mathbf{if}\;b \leq -9 \cdot 10^{+40}:\\ \;\;\;\;\frac{b \cdot b}{y} \cdot \frac{x}{a} + \frac{t_1}{y \cdot a}\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-234}:\\ \;\;\;\;\frac{\frac{t_1}{y}}{a}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* x b))))
   (if (<= b -9e+40)
     (+ (* (/ (* b b) y) (/ x a)) (/ t_1 (* y a)))
     (if (<= b -4.1e-234)
       (/ (/ t_1 y) a)
       (if (<= b 1.05e-169)
         (/ (- (* x b)) (* y a))
         (/ x (* y (* a (+ 1.0 b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (x * b);
	double tmp;
	if (b <= -9e+40) {
		tmp = (((b * b) / y) * (x / a)) + (t_1 / (y * a));
	} else if (b <= -4.1e-234) {
		tmp = (t_1 / y) / a;
	} else if (b <= 1.05e-169) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * b)
    if (b <= (-9d+40)) then
        tmp = (((b * b) / y) * (x / a)) + (t_1 / (y * a))
    else if (b <= (-4.1d-234)) then
        tmp = (t_1 / y) / a
    else if (b <= 1.05d-169) then
        tmp = -(x * b) / (y * a)
    else
        tmp = x / (y * (a * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (x * b);
	double tmp;
	if (b <= -9e+40) {
		tmp = (((b * b) / y) * (x / a)) + (t_1 / (y * a));
	} else if (b <= -4.1e-234) {
		tmp = (t_1 / y) / a;
	} else if (b <= 1.05e-169) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (x * b)
	tmp = 0
	if b <= -9e+40:
		tmp = (((b * b) / y) * (x / a)) + (t_1 / (y * a))
	elif b <= -4.1e-234:
		tmp = (t_1 / y) / a
	elif b <= 1.05e-169:
		tmp = -(x * b) / (y * a)
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(x * b))
	tmp = 0.0
	if (b <= -9e+40)
		tmp = Float64(Float64(Float64(Float64(b * b) / y) * Float64(x / a)) + Float64(t_1 / Float64(y * a)));
	elseif (b <= -4.1e-234)
		tmp = Float64(Float64(t_1 / y) / a);
	elseif (b <= 1.05e-169)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (x * b);
	tmp = 0.0;
	if (b <= -9e+40)
		tmp = (((b * b) / y) * (x / a)) + (t_1 / (y * a));
	elseif (b <= -4.1e-234)
		tmp = (t_1 / y) / a;
	elseif (b <= 1.05e-169)
		tmp = -(x * b) / (y * a);
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+40], N[(N[(N[(N[(b * b), $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.1e-234], N[(N[(t$95$1 / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.05e-169], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.00000000000000064e40

   1. Initial program 100.0%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. +-commutative 88.7%

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

      4. associate--l+ 88.7%

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

      5. exp-sum 73.6%

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

      6. *-commutative 73.6%

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

      7. exp-to-pow 73.6%

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

      8. sub-neg 73.6%

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

      9. metadata-eval 73.6%

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

      10. exp-diff 49.1%

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

      11. *-commutative 49.1%

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

      12. exp-to-pow 49.1%

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

   3. Simplified 49.1%

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

   4. Taylor expanded in t around 0 68.0%

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

   5. Taylor expanded in y around 0 79.6%

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

   6. Taylor expanded in b around 0 10.7%

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

   7. Taylor expanded in b around 0 59.5%

      \[\leadsto \color{blue}{\frac{{b}^{2} \cdot x}{a \cdot y} + \left(\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}\right)} \]
   8. Step-by-step derivation

      1. associate-+r+ 59.5%

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

      2. associate-*r/ 59.5%

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

      3. *-commutative 59.5%

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

      4. associate-*r/ 59.5%

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

      5. times-frac 59.2%

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

      6. neg-mul-1 59.2%

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

      7. *-commutative 59.2%

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

      8. *-commutative 59.2%

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

      9. associate-+r+ 59.2%

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

      10. times-frac 59.3%

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

      11. unpow2 59.3%

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

      12. unsub-neg 59.3%

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

      13. associate-/r* 59.3%

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

      14. associate-*l/ 61.3%

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

   9. Simplified 59.3%

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

   if -9.00000000000000064e40 < b < -4.10000000000000011e-234

   1. Initial program 96.3%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. +-commutative 85.5%

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

      4. associate--l+ 85.5%

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

      5. exp-sum 76.7%

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

      6. *-commutative 76.7%

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

      7. exp-to-pow 77.8%

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

      8. sub-neg 77.8%

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

      9. metadata-eval 77.8%

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

      10. exp-diff 77.8%

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

      11. *-commutative 77.8%

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

      12. exp-to-pow 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in t around 0 63.9%

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

   5. Taylor expanded in y around 0 44.1%

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

   6. Taylor expanded in b around 0 36.8%

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

   7. Taylor expanded in b around 0 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-*r/ 35.5%

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

      3. *-commutative 35.5%

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

      4. associate-*r/ 35.5%

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

      5. metadata-eval 35.5%

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

      6. times-frac 35.4%

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

      7. cancel-sign-sub-inv 35.4%

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

      8. associate-/r* 38.2%

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

      9. *-lft-identity 38.2%

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

      10. associate-*l/ 39.7%

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

      11. div-sub 39.7%

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

      12. associate-*r/ 41.1%

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

      13. div-sub 41.1%

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

      14. *-commutative 41.1%

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

   9. Simplified 41.1%

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

   if -4.10000000000000011e-234 < b < 1.05e-169

   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/ 93.2%

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

      2. *-commutative 93.2%

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

      3. +-commutative 93.2%

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

      4. associate--l+ 93.2%

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

      5. exp-sum 79.8%

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

      6. *-commutative 79.8%

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

      7. exp-to-pow 80.8%

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

      8. sub-neg 80.8%

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

      9. metadata-eval 80.8%

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

      10. exp-diff 80.8%

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

      11. *-commutative 80.8%

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

      12. exp-to-pow 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 63.2%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

      4. times-frac 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in b around -inf 45.1%

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

   if 1.05e-169 < b

   1. Initial program 99.5%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 72.3%

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

      6. *-commutative 72.3%

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

      7. exp-to-pow 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. exp-diff 63.3%

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

      11. *-commutative 63.3%

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

      12. exp-to-pow 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in t around 0 68.7%

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

      1. times-frac 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in b around 0 55.1%

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

   8. Taylor expanded in y around 0 41.0%

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

      1. +-commutative 41.0%

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

   10. Simplified 41.0%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+40}:\\ \;\;\;\;\frac{b \cdot b}{y} \cdot \frac{x}{a} + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-234}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-169}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 10: 41.4% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 10^{-168}:\\ \;\;\;\;\frac{y \cdot \frac{x}{y} - a \cdot \left(x \cdot \frac{b}{a}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1e-168)
   (/ (- (* y (/ x y)) (* a (* x (/ b a)))) (* y a))
   (/ x (* y (* a (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1e-168) {
		tmp = ((y * (x / y)) - (a * (x * (b / a)))) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1d-168) then
        tmp = ((y * (x / y)) - (a * (x * (b / a)))) / (y * a)
    else
        tmp = x / (y * (a * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1e-168) {
		tmp = ((y * (x / y)) - (a * (x * (b / a)))) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1e-168:
		tmp = ((y * (x / y)) - (a * (x * (b / a)))) / (y * a)
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1e-168)
		tmp = Float64(Float64(Float64(y * Float64(x / y)) - Float64(a * Float64(x * Float64(b / a)))) / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1e-168)
		tmp = ((y * (x / y)) - (a * (x * (b / a)))) / (y * a);
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1e-168], N[(N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1e-168

   1. Initial program 98.1%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 76.4%

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

      6. *-commutative 76.4%

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

      7. exp-to-pow 77.1%

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

      8. sub-neg 77.1%

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

      9. metadata-eval 77.1%

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

      10. exp-diff 68.9%

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

      11. *-commutative 68.9%

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

      12. exp-to-pow 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in t around 0 65.1%

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

   5. Taylor expanded in y around 0 53.1%

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

   6. Taylor expanded in b around 0 35.5%

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

      1. +-commutative 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. times-frac 37.2%

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

   8. Simplified 37.2%

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

      1. associate-/r* 37.7%

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

      2. associate-*r/ 39.7%

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

      3. frac-sub 42.6%

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

      4. *-commutative 42.6%

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

   10. Applied egg-rr 42.6%

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

   if 1e-168 < b

   1. Initial program 99.5%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 72.3%

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

      6. *-commutative 72.3%

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

      7. exp-to-pow 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. exp-diff 63.3%

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

      11. *-commutative 63.3%

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

      12. exp-to-pow 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in t around 0 68.7%

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

      1. times-frac 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in b around 0 55.1%

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

   8. Taylor expanded in y around 0 41.0%

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

      1. +-commutative 41.0%

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

   10. Simplified 41.0%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 10^{-168}:\\ \;\;\;\;\frac{y \cdot \frac{x}{y} - a \cdot \left(x \cdot \frac{b}{a}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 11: 37.3% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-230}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- (/ b a)))))
   (if (<= b -5.1e-40)
     t_1
     (if (<= b -1.65e-230)
       (* (/ x y) (/ 1.0 a))
       (if (<= b 1.36e-245)
         t_1
         (if (<= b 2.2e-12) (/ (/ x y) a) (/ x (* y (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * -(b / a);
	double tmp;
	if (b <= -5.1e-40) {
		tmp = t_1;
	} else if (b <= -1.65e-230) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 1.36e-245) {
		tmp = t_1;
	} else if (b <= 2.2e-12) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * -(b / a)
    if (b <= (-5.1d-40)) then
        tmp = t_1
    else if (b <= (-1.65d-230)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 1.36d-245) then
        tmp = t_1
    else if (b <= 2.2d-12) then
        tmp = (x / y) / a
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) * -(b / a);
	double tmp;
	if (b <= -5.1e-40) {
		tmp = t_1;
	} else if (b <= -1.65e-230) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 1.36e-245) {
		tmp = t_1;
	} else if (b <= 2.2e-12) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) * -(b / a)
	tmp = 0
	if b <= -5.1e-40:
		tmp = t_1
	elif b <= -1.65e-230:
		tmp = (x / y) * (1.0 / a)
	elif b <= 1.36e-245:
		tmp = t_1
	elif b <= 2.2e-12:
		tmp = (x / y) / a
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) * Float64(-Float64(b / a)))
	tmp = 0.0
	if (b <= -5.1e-40)
		tmp = t_1;
	elseif (b <= -1.65e-230)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 1.36e-245)
		tmp = t_1;
	elseif (b <= 2.2e-12)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) * -(b / a);
	tmp = 0.0;
	if (b <= -5.1e-40)
		tmp = t_1;
	elseif (b <= -1.65e-230)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 1.36e-245)
		tmp = t_1;
	elseif (b <= 2.2e-12)
		tmp = (x / y) / a;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-N[(b / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[b, -5.1e-40], t$95$1, If[LessEqual[b, -1.65e-230], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.36e-245], t$95$1, If[LessEqual[b, 2.2e-12], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.10000000000000037e-40 or -1.64999999999999997e-230 < b < 1.3600000000000001e-245

   1. Initial program 99.5%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

      3. +-commutative 88.1%

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

      4. associate--l+ 88.1%

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

      5. exp-sum 73.6%

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

      6. *-commutative 73.6%

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

      7. exp-to-pow 73.8%

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

      8. sub-neg 73.8%

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

      9. metadata-eval 73.8%

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

      10. exp-diff 60.3%

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

      11. *-commutative 60.3%

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

      12. exp-to-pow 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in t around 0 62.0%

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

   5. Taylor expanded in y around 0 59.7%

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

   6. Taylor expanded in b around 0 30.7%

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

      1. +-commutative 30.7%

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

      2. mul-1-neg 30.7%

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

      3. unsub-neg 30.7%

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

      4. times-frac 34.6%

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

   8. Simplified 34.6%

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

   9. Taylor expanded in b around inf 34.5%

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

       1. times-frac 38.4%

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

       2. neg-mul-1 38.4%

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

       3. *-commutative 38.4%

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

       4. distribute-lft-neg-in 38.4%

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

       5. distribute-neg-frac 38.4%

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

   11. Simplified 38.4%

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

   if -5.10000000000000037e-40 < b < -1.64999999999999997e-230

   1. Initial program 95.3%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. +-commutative 86.8%

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

      4. associate--l+ 86.8%

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

      5. exp-sum 79.0%

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

      6. *-commutative 79.0%

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

      7. exp-to-pow 80.3%

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

      8. sub-neg 80.3%

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

      9. metadata-eval 80.3%

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

      10. exp-diff 80.3%

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

      11. *-commutative 80.3%

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

      12. exp-to-pow 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around 0 67.3%

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

   5. Taylor expanded in y around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

      1. *-un-lft-identity 43.7%

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

      2. *-commutative 43.7%

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

      3. times-frac 47.4%

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

   10. Applied egg-rr 47.4%

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

   if 1.3600000000000001e-245 < b < 2.19999999999999992e-12

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0 73.5%

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

      1. mul-1-neg 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in y around 0 41.2%

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

      1. associate-/l* 47.3%

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

      2. +-commutative 47.3%

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

      3. distribute-neg-in 47.3%

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

      4. neg-mul-1 47.3%

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

      5. sub-neg 47.3%

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

      6. associate-/l* 41.2%

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

      7. *-commutative 41.2%

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

      8. exp-diff 41.2%

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

      9. neg-mul-1 41.2%

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

      10. associate-*r/ 41.2%

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

      11. log-rec 41.2%

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

      12. rem-exp-log 42.4%

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

      13. associate-*r/ 42.4%

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

      14. *-rgt-identity 42.4%

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

      15. associate-/r* 42.4%

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

      16. *-commutative 42.4%

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

   7. Simplified 44.4%

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

   8. Taylor expanded in b around 0 44.4%

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

   if 2.19999999999999992e-12 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

      3. +-commutative 91.9%

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

      4. associate--l+ 91.9%

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

      5. exp-sum 71.0%

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

      6. *-commutative 71.0%

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

      7. exp-to-pow 71.0%

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

      8. sub-neg 71.0%

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

      9. metadata-eval 71.0%

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

      10. exp-diff 56.5%

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

      11. *-commutative 56.5%

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

      12. exp-to-pow 56.5%

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

   3. Simplified 56.5%

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

   4. Taylor expanded in t around 0 66.4%

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

   5. Taylor expanded in y around 0 74.6%

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

   6. Taylor expanded in b around 0 39.0%

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

   7. Taylor expanded in b around -inf 39.5%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-230}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 12: 36.5% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-169}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.9e-41)
   (* (/ x y) (- (/ b a)))
   (if (<= b -3.5e-235)
     (* (/ x y) (/ 1.0 a))
     (if (<= b 1.26e-169)
       (/ (- (* x b)) (* y a))
       (if (<= b 5.5e+31) (/ x (* y a)) (/ x (* y (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.9e-41) {
		tmp = (x / y) * -(b / a);
	} else if (b <= -3.5e-235) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 1.26e-169) {
		tmp = -(x * b) / (y * a);
	} else if (b <= 5.5e+31) {
		tmp = x / (y * a);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.9d-41)) then
        tmp = (x / y) * -(b / a)
    else if (b <= (-3.5d-235)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 1.26d-169) then
        tmp = -(x * b) / (y * a)
    else if (b <= 5.5d+31) then
        tmp = x / (y * a)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.9e-41) {
		tmp = (x / y) * -(b / a);
	} else if (b <= -3.5e-235) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 1.26e-169) {
		tmp = -(x * b) / (y * a);
	} else if (b <= 5.5e+31) {
		tmp = x / (y * a);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.9e-41:
		tmp = (x / y) * -(b / a)
	elif b <= -3.5e-235:
		tmp = (x / y) * (1.0 / a)
	elif b <= 1.26e-169:
		tmp = -(x * b) / (y * a)
	elif b <= 5.5e+31:
		tmp = x / (y * a)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.9e-41)
		tmp = Float64(Float64(x / y) * Float64(-Float64(b / a)));
	elseif (b <= -3.5e-235)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 1.26e-169)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	elseif (b <= 5.5e+31)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.9e-41)
		tmp = (x / y) * -(b / a);
	elseif (b <= -3.5e-235)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 1.26e-169)
		tmp = -(x * b) / (y * a);
	elseif (b <= 5.5e+31)
		tmp = x / (y * a);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.9e-41], N[(N[(x / y), $MachinePrecision] * (-N[(b / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, -3.5e-235], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.26e-169], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+31], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.90000000000000006e-41

   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/ 87.0%

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

      2. *-commutative 87.0%

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

      3. +-commutative 87.0%

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

      4. associate--l+ 87.0%

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

      5. exp-sum 72.7%

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

      6. *-commutative 72.7%

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

      7. exp-to-pow 72.8%

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

      8. sub-neg 72.8%

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

      9. metadata-eval 72.8%

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

      10. exp-diff 54.3%

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

      11. *-commutative 54.3%

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

      12. exp-to-pow 54.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in t around 0 64.6%

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

   5. Taylor expanded in y around 0 71.2%

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

   6. Taylor expanded in b around 0 31.4%

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

      1. +-commutative 31.4%

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

      2. mul-1-neg 31.4%

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

      3. unsub-neg 31.4%

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

      4. times-frac 36.8%

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

   8. Simplified 36.8%

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

   9. Taylor expanded in b around inf 31.0%

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

       1. times-frac 37.7%

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

       2. neg-mul-1 37.7%

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

       3. *-commutative 37.7%

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

       4. distribute-lft-neg-in 37.7%

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

       5. distribute-neg-frac 37.7%

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

   11. Simplified 37.7%

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

   if -8.90000000000000006e-41 < b < -3.4999999999999999e-235

   1. Initial program 95.3%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. +-commutative 86.8%

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

      4. associate--l+ 86.8%

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

      5. exp-sum 79.0%

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

      6. *-commutative 79.0%

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

      7. exp-to-pow 80.3%

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

      8. sub-neg 80.3%

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

      9. metadata-eval 80.3%

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

      10. exp-diff 80.3%

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

      11. *-commutative 80.3%

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

      12. exp-to-pow 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around 0 67.3%

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

   5. Taylor expanded in y around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

      1. *-un-lft-identity 43.7%

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

      2. *-commutative 43.7%

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

      3. times-frac 47.4%

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

   10. Applied egg-rr 47.4%

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

   if -3.4999999999999999e-235 < b < 1.26e-169

   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/ 93.2%

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

      2. *-commutative 93.2%

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

      3. +-commutative 93.2%

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

      4. associate--l+ 93.2%

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

      5. exp-sum 79.8%

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

      6. *-commutative 79.8%

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

      7. exp-to-pow 80.8%

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

      8. sub-neg 80.8%

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

      9. metadata-eval 80.8%

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

      10. exp-diff 80.8%

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

      11. *-commutative 80.8%

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

      12. exp-to-pow 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 63.2%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

      4. times-frac 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in b around -inf 45.1%

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

   if 1.26e-169 < b < 5.50000000000000002e31

   1. Initial program 98.8%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

      3. +-commutative 85.3%

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

      4. associate--l+ 85.3%

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

      5. exp-sum 78.2%

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

      6. *-commutative 78.2%

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

      7. exp-to-pow 78.6%

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

      8. sub-neg 78.6%

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

      9. metadata-eval 78.6%

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

      10. exp-diff 71.5%

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

      11. *-commutative 71.5%

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

      12. exp-to-pow 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in t around 0 69.5%

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

   5. Taylor expanded in y around 0 44.7%

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

   6. Taylor expanded in b around 0 42.5%

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

      1. *-commutative 42.5%

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

   8. Simplified 42.5%

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

   if 5.50000000000000002e31 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 91.1%

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

      2. *-commutative 91.1%

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

      3. +-commutative 91.1%

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

      4. associate--l+ 91.1%

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

      5. exp-sum 67.9%

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

      6. *-commutative 67.9%

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

      7. exp-to-pow 67.9%

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

      8. sub-neg 67.9%

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

      9. metadata-eval 67.9%

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

      10. exp-diff 57.1%

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

      11. *-commutative 57.1%

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

      12. exp-to-pow 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in t around 0 68.1%

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

   5. Taylor expanded in y around 0 77.1%

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

   6. Taylor expanded in b around 0 39.4%

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

   7. Taylor expanded in b around -inf 39.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-169}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 13: 36.3% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-232}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.1e-40)
   (* (/ x y) (- (/ b a)))
   (if (<= b -4.8e-232)
     (* (/ x y) (/ 1.0 a))
     (if (<= b 6.6e-170) (/ (- (* x b)) (* y a)) (/ x (* a (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.1e-40) {
		tmp = (x / y) * -(b / a);
	} else if (b <= -4.8e-232) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 6.6e-170) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.1d-40)) then
        tmp = (x / y) * -(b / a)
    else if (b <= (-4.8d-232)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 6.6d-170) then
        tmp = -(x * b) / (y * a)
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.1e-40) {
		tmp = (x / y) * -(b / a);
	} else if (b <= -4.8e-232) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 6.6e-170) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.1e-40:
		tmp = (x / y) * -(b / a)
	elif b <= -4.8e-232:
		tmp = (x / y) * (1.0 / a)
	elif b <= 6.6e-170:
		tmp = -(x * b) / (y * a)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.1e-40)
		tmp = Float64(Float64(x / y) * Float64(-Float64(b / a)));
	elseif (b <= -4.8e-232)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 6.6e-170)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.1e-40)
		tmp = (x / y) * -(b / a);
	elseif (b <= -4.8e-232)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 6.6e-170)
		tmp = -(x * b) / (y * a);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.1e-40], N[(N[(x / y), $MachinePrecision] * (-N[(b / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, -4.8e-232], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e-170], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.10000000000000037e-40

   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/ 87.0%

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

      2. *-commutative 87.0%

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

      3. +-commutative 87.0%

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

      4. associate--l+ 87.0%

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

      5. exp-sum 72.7%

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

      6. *-commutative 72.7%

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

      7. exp-to-pow 72.8%

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

      8. sub-neg 72.8%

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

      9. metadata-eval 72.8%

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

      10. exp-diff 54.3%

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

      11. *-commutative 54.3%

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

      12. exp-to-pow 54.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in t around 0 64.6%

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

   5. Taylor expanded in y around 0 71.2%

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

   6. Taylor expanded in b around 0 31.4%

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

      1. +-commutative 31.4%

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

      2. mul-1-neg 31.4%

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

      3. unsub-neg 31.4%

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

      4. times-frac 36.8%

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

   8. Simplified 36.8%

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

   9. Taylor expanded in b around inf 31.0%

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

       1. times-frac 37.7%

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

       2. neg-mul-1 37.7%

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

       3. *-commutative 37.7%

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

       4. distribute-lft-neg-in 37.7%

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

       5. distribute-neg-frac 37.7%

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

   11. Simplified 37.7%

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

   if -5.10000000000000037e-40 < b < -4.79999999999999998e-232

   1. Initial program 95.3%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. +-commutative 86.8%

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

      4. associate--l+ 86.8%

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

      5. exp-sum 79.0%

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

      6. *-commutative 79.0%

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

      7. exp-to-pow 80.3%

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

      8. sub-neg 80.3%

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

      9. metadata-eval 80.3%

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

      10. exp-diff 80.3%

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

      11. *-commutative 80.3%

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

      12. exp-to-pow 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around 0 67.3%

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

   5. Taylor expanded in y around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

      1. *-un-lft-identity 43.7%

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

      2. *-commutative 43.7%

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

      3. times-frac 47.4%

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

   10. Applied egg-rr 47.4%

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

   if -4.79999999999999998e-232 < b < 6.60000000000000007e-170

   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/ 93.2%

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

      2. *-commutative 93.2%

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

      3. +-commutative 93.2%

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

      4. associate--l+ 93.2%

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

      5. exp-sum 79.8%

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

      6. *-commutative 79.8%

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

      7. exp-to-pow 80.8%

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

      8. sub-neg 80.8%

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

      9. metadata-eval 80.8%

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

      10. exp-diff 80.8%

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

      11. *-commutative 80.8%

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

      12. exp-to-pow 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 63.2%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

      4. times-frac 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in b around -inf 45.1%

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

   if 6.60000000000000007e-170 < b

   1. Initial program 99.5%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 72.3%

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

      6. *-commutative 72.3%

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

      7. exp-to-pow 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. exp-diff 63.3%

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

      11. *-commutative 63.3%

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

      12. exp-to-pow 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in t around 0 68.7%

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

   5. Taylor expanded in y around 0 63.2%

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

   6. Taylor expanded in b around 0 40.7%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-232}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 36.6% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e-40)
   (* (/ x y) (- (/ b a)))
   (if (<= b -3.2e-235)
     (* (/ x y) (/ 1.0 a))
     (if (<= b 4.5e-169)
       (/ (- (* x b)) (* y a))
       (/ x (* y (* a (+ 1.0 b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e-40) {
		tmp = (x / y) * -(b / a);
	} else if (b <= -3.2e-235) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 4.5e-169) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d-40)) then
        tmp = (x / y) * -(b / a)
    else if (b <= (-3.2d-235)) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 4.5d-169) then
        tmp = -(x * b) / (y * a)
    else
        tmp = x / (y * (a * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e-40) {
		tmp = (x / y) * -(b / a);
	} else if (b <= -3.2e-235) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 4.5e-169) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e-40:
		tmp = (x / y) * -(b / a)
	elif b <= -3.2e-235:
		tmp = (x / y) * (1.0 / a)
	elif b <= 4.5e-169:
		tmp = -(x * b) / (y * a)
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e-40)
		tmp = Float64(Float64(x / y) * Float64(-Float64(b / a)));
	elseif (b <= -3.2e-235)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 4.5e-169)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e-40)
		tmp = (x / y) * -(b / a);
	elseif (b <= -3.2e-235)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 4.5e-169)
		tmp = -(x * b) / (y * a);
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e-40], N[(N[(x / y), $MachinePrecision] * (-N[(b / a), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, -3.2e-235], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e-169], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.2000000000000003e-40

   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/ 87.0%

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

      2. *-commutative 87.0%

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

      3. +-commutative 87.0%

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

      4. associate--l+ 87.0%

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

      5. exp-sum 72.7%

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

      6. *-commutative 72.7%

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

      7. exp-to-pow 72.8%

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

      8. sub-neg 72.8%

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

      9. metadata-eval 72.8%

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

      10. exp-diff 54.3%

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

      11. *-commutative 54.3%

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

      12. exp-to-pow 54.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in t around 0 64.6%

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

   5. Taylor expanded in y around 0 71.2%

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

   6. Taylor expanded in b around 0 31.4%

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

      1. +-commutative 31.4%

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

      2. mul-1-neg 31.4%

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

      3. unsub-neg 31.4%

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

      4. times-frac 36.8%

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

   8. Simplified 36.8%

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

   9. Taylor expanded in b around inf 31.0%

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

       1. times-frac 37.7%

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

       2. neg-mul-1 37.7%

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

       3. *-commutative 37.7%

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

       4. distribute-lft-neg-in 37.7%

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

       5. distribute-neg-frac 37.7%

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

   11. Simplified 37.7%

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

   if -5.2000000000000003e-40 < b < -3.2000000000000001e-235

   1. Initial program 95.3%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. +-commutative 86.8%

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

      4. associate--l+ 86.8%

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

      5. exp-sum 79.0%

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

      6. *-commutative 79.0%

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

      7. exp-to-pow 80.3%

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

      8. sub-neg 80.3%

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

      9. metadata-eval 80.3%

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

      10. exp-diff 80.3%

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

      11. *-commutative 80.3%

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

      12. exp-to-pow 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around 0 67.3%

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

   5. Taylor expanded in y around 0 43.7%

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

   6. Taylor expanded in b around 0 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

      1. *-un-lft-identity 43.7%

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

      2. *-commutative 43.7%

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

      3. times-frac 47.4%

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

   10. Applied egg-rr 47.4%

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

   if -3.2000000000000001e-235 < b < 4.4999999999999999e-169

   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/ 93.2%

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

      2. *-commutative 93.2%

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

      3. +-commutative 93.2%

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

      4. associate--l+ 93.2%

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

      5. exp-sum 79.8%

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

      6. *-commutative 79.8%

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

      7. exp-to-pow 80.8%

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

      8. sub-neg 80.8%

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

      9. metadata-eval 80.8%

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

      10. exp-diff 80.8%

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

      11. *-commutative 80.8%

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

      12. exp-to-pow 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 63.2%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

      4. times-frac 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in b around -inf 45.1%

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

   if 4.4999999999999999e-169 < b

   1. Initial program 99.5%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 72.3%

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

      6. *-commutative 72.3%

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

      7. exp-to-pow 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. exp-diff 63.3%

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

      11. *-commutative 63.3%

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

      12. exp-to-pow 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in t around 0 68.7%

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

      1. times-frac 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in b around 0 55.1%

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

   8. Taylor expanded in y around 0 41.0%

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

      1. +-commutative 41.0%

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

   10. Simplified 41.0%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 15: 38.0% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-234}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e-234)
   (/ (/ (- x (* x b)) y) a)
   (if (<= b 6.3e-170) (/ (- (* x b)) (* y a)) (/ x (* y (* a (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e-234) {
		tmp = ((x - (x * b)) / y) / a;
	} else if (b <= 6.3e-170) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.3d-234)) then
        tmp = ((x - (x * b)) / y) / a
    else if (b <= 6.3d-170) then
        tmp = -(x * b) / (y * a)
    else
        tmp = x / (y * (a * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e-234) {
		tmp = ((x - (x * b)) / y) / a;
	} else if (b <= 6.3e-170) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e-234:
		tmp = ((x - (x * b)) / y) / a
	elif b <= 6.3e-170:
		tmp = -(x * b) / (y * a)
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e-234)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / y) / a);
	elseif (b <= 6.3e-170)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.3e-234)
		tmp = ((x - (x * b)) / y) / a;
	elseif (b <= 6.3e-170)
		tmp = -(x * b) / (y * a);
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e-234], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 6.3e-170], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2999999999999999e-234

   1. Initial program 97.9%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

      3. +-commutative 86.9%

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

      4. associate--l+ 86.9%

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

      5. exp-sum 75.4%

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

      6. *-commutative 75.4%

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

      7. exp-to-pow 76.0%

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

      8. sub-neg 76.0%

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

      9. metadata-eval 76.0%

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

      10. exp-diff 65.2%

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

      11. *-commutative 65.2%

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

      12. exp-to-pow 65.2%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in t around 0 65.7%

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

   5. Taylor expanded in y around 0 59.6%

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

   6. Taylor expanded in b around 0 25.4%

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

   7. Taylor expanded in b around 0 36.6%

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

      1. *-commutative 36.6%

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

      2. associate-*r/ 36.6%

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

      3. *-commutative 36.6%

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

      4. associate-*r/ 36.6%

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

      5. metadata-eval 36.6%

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

      6. times-frac 38.8%

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

      7. cancel-sign-sub-inv 38.8%

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

      8. associate-/r* 40.4%

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

      9. *-lft-identity 40.4%

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

      10. associate-*l/ 39.1%

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

      11. div-sub 39.1%

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

      12. associate-*r/ 41.4%

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

      13. div-sub 41.4%

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

      14. *-commutative 41.4%

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

   9. Simplified 41.4%

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

   if -2.2999999999999999e-234 < b < 6.3000000000000002e-170

   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/ 93.2%

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

      2. *-commutative 93.2%

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

      3. +-commutative 93.2%

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

      4. associate--l+ 93.2%

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

      5. exp-sum 79.8%

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

      6. *-commutative 79.8%

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

      7. exp-to-pow 80.8%

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

      8. sub-neg 80.8%

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

      9. metadata-eval 80.8%

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

      10. exp-diff 80.8%

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

      11. *-commutative 80.8%

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

      12. exp-to-pow 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 63.2%

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

   5. Taylor expanded in y around 0 31.7%

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

   6. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

      4. times-frac 31.7%

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

   8. Simplified 31.7%

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

   9. Taylor expanded in b around -inf 45.1%

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

   if 6.3000000000000002e-170 < b

   1. Initial program 99.5%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. +-commutative 88.6%

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

      4. associate--l+ 88.6%

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

      5. exp-sum 72.3%

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

      6. *-commutative 72.3%

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

      7. exp-to-pow 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. exp-diff 63.3%

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

      11. *-commutative 63.3%

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

      12. exp-to-pow 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in t around 0 68.7%

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

      1. times-frac 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in b around 0 55.1%

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

   8. Taylor expanded in y around 0 41.0%

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

      1. +-commutative 41.0%

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

   10. Simplified 41.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-234}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 6.3 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 16: 37.9% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.6e-307)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 8e-170) (/ (- (* x b)) (* y a)) (/ x (* y (* a (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e-307) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 8e-170) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.6d-307)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 8d-170) then
        tmp = -(x * b) / (y * a)
    else
        tmp = x / (y * (a * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e-307) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 8e-170) {
		tmp = -(x * b) / (y * a);
	} else {
		tmp = x / (y * (a * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.6e-307:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 8e-170:
		tmp = -(x * b) / (y * a)
	else:
		tmp = x / (y * (a * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.6e-307)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 8e-170)
		tmp = Float64(Float64(-Float64(x * b)) / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.6e-307)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 8e-170)
		tmp = -(x * b) / (y * a);
	else
		tmp = x / (y * (a * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.6e-307], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 8e-170], N[((-N[(x * b), $MachinePrecision]) / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.59999999999999971e-307

   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/ 88.1%

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

      2. *-commutative 88.1%

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

      3. +-commutative 88.1%

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

      4. associate--l+ 88.1%

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

      5. exp-sum 75.4%

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

      6. *-commutative 75.4%

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

      7. exp-to-pow 76.1%

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

      8. sub-neg 76.1%

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

      9. metadata-eval 76.1%

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

      10. exp-diff 66.4%

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

      11. *-commutative 66.4%

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

      12. exp-to-pow 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in t around 0 63.9%

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

   5. Taylor expanded in y around 0 57.0%

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

   6. Taylor expanded in b around 0 36.3%

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

      1. +-commutative 36.3%

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

      2. mul-1-neg 36.3%

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

      3. unsub-neg 36.3%

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

      4. times-frac 38.3%

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

   8. Simplified 38.3%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{b}{a} \cdot \frac{x}{y}} \]

   9. Taylor expanded in y around 0 42.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} - \frac{b \cdot x}{a}}{y}} \]

   if -7.59999999999999971e-307 < b < 7.99999999999999987e-170

   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/ 89.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 89.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 89.9%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 89.9%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 81.9%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 81.9%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 82.9%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 82.9%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 82.9%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 82.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 82.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 82.9%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 71.9%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 31.0%

      \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   6. Taylor expanded in b around 0 31.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}} \]
   7. Step-by-step derivation

      1. +-commutative 31.0%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 31.0%

         \[\leadsto \frac{x}{y \cdot a} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 31.0%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{b \cdot x}{a \cdot y}} \]

      4. times-frac 31.0%

         \[\leadsto \frac{x}{y \cdot a} - \color{blue}{\frac{b}{a} \cdot \frac{x}{y}} \]

   8. Simplified 31.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{b}{a} \cdot \frac{x}{y}} \]

   9. Taylor expanded in b around -inf 51.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y \cdot a}} \]

   if 7.99999999999999987e-170 < b

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 88.6%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 72.3%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 72.3%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 72.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 72.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 72.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 63.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 63.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 63.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 63.3%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 68.7%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. times-frac 66.7%

         \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

   6. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}} \]

   7. Taylor expanded in b around 0 55.1%

      \[\leadsto \frac{{z}^{y}}{a} \cdot \frac{x}{\color{blue}{y \cdot b + y}} \]

   8. Taylor expanded in y around 0 41.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}} \]
   9. Step-by-step derivation

      1. +-commutative 41.0%

         \[\leadsto \frac{x}{y \cdot \left(a \cdot \color{blue}{\left(b + 1\right)}\right)} \]

   10. Simplified 41.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot \left(b + 1\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 17: 32.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.15e-119) (/ (/ x y) a) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.15e-119) {
		tmp = (x / y) / a;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.15d-119) then
        tmp = (x / y) / a
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.15e-119) {
		tmp = (x / y) / a;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.15e-119:
		tmp = (x / y) / a
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.15e-119)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.15e-119)
		tmp = (x / y) / a;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.15e-119], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.14999999999999997e-119

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 82.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 48.1%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 50.1%

         \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)}}{\frac{y}{x}}} \]

      2. +-commutative 50.1%

         \[\leadsto \frac{e^{-\color{blue}{\left(\log a + b\right)}}}{\frac{y}{x}} \]

      3. distribute-neg-in 50.1%

         \[\leadsto \frac{e^{\color{blue}{\left(-\log a\right) + \left(-b\right)}}}{\frac{y}{x}} \]

      4. neg-mul-1 50.1%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a} + \left(-b\right)}}{\frac{y}{x}} \]

      5. sub-neg 50.1%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a - b}}}{\frac{y}{x}} \]

      6. associate-/l* 48.1%

         \[\leadsto \color{blue}{\frac{e^{-1 \cdot \log a - b} \cdot x}{y}} \]

      7. *-commutative 48.1%

         \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]

      8. exp-diff 48.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}}}{y} \]

      9. neg-mul-1 48.1%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{-\log a}}}{e^{b}}}{y} \]

      10. associate-*r/ 43.2%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{-\log a}}{e^{b}}}}{y} \]

      11. log-rec 43.2%

          \[\leadsto \frac{\frac{x \cdot e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}}}{y} \]

      12. rem-exp-log 43.4%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

      13. associate-*r/ 43.4%

          \[\leadsto \frac{\frac{\color{blue}{\frac{x \cdot 1}{a}}}{e^{b}}}{y} \]

      14. *-rgt-identity 43.4%

          \[\leadsto \frac{\frac{\frac{\color{blue}{x}}{a}}{e^{b}}}{y} \]

      15. associate-/r* 43.4%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      16. *-commutative 43.4%

          \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

   7. Simplified 48.0%

      \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   8. Taylor expanded in b around 0 31.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if 1.14999999999999997e-119 < a

   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/ 87.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 74.8%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 74.8%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 75.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 75.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 75.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 67.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 67.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 67.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 62.7%

      \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   6. Taylor expanded in b around 0 34.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. div-inv 35.0%

         \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

   10. Applied egg-rr 35.0%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]

Alternative 18: 35.9% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.3e-12) (/ (/ x y) a) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e-12) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.3d-12) then
        tmp = (x / y) / a
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e-12) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.3e-12:
		tmp = (x / y) / a
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.3e-12)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.3e-12)
		tmp = (x / y) / a;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.3e-12], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.29999999999999989e-12

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 76.2%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 76.2%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 76.2%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 49.9%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 50.5%

         \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)}}{\frac{y}{x}}} \]

      2. +-commutative 50.5%

         \[\leadsto \frac{e^{-\color{blue}{\left(\log a + b\right)}}}{\frac{y}{x}} \]

      3. distribute-neg-in 50.5%

         \[\leadsto \frac{e^{\color{blue}{\left(-\log a\right) + \left(-b\right)}}}{\frac{y}{x}} \]

      4. neg-mul-1 50.5%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a} + \left(-b\right)}}{\frac{y}{x}} \]

      5. sub-neg 50.5%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a - b}}}{\frac{y}{x}} \]

      6. associate-/l* 49.9%

         \[\leadsto \color{blue}{\frac{e^{-1 \cdot \log a - b} \cdot x}{y}} \]

      7. *-commutative 49.9%

         \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]

      8. exp-diff 49.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}}}{y} \]

      9. neg-mul-1 49.9%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{-\log a}}}{e^{b}}}{y} \]

      10. associate-*r/ 47.3%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{-\log a}}{e^{b}}}}{y} \]

      11. log-rec 47.3%

          \[\leadsto \frac{\frac{x \cdot e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}}}{y} \]

      12. rem-exp-log 47.8%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

      13. associate-*r/ 47.8%

          \[\leadsto \frac{\frac{\color{blue}{\frac{x \cdot 1}{a}}}{e^{b}}}{y} \]

      14. *-rgt-identity 47.8%

          \[\leadsto \frac{\frac{\frac{\color{blue}{x}}{a}}{e^{b}}}{y} \]

      15. associate-/r* 47.8%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      16. *-commutative 47.8%

          \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

   7. Simplified 49.2%

      \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   8. Taylor expanded in b around 0 33.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if 2.29999999999999989e-12 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 91.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 91.9%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 91.9%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 71.0%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 71.0%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 71.0%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 71.0%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 71.0%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 56.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 56.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 56.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 56.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 66.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 74.6%

      \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   6. Taylor expanded in b around 0 39.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b + y\right)}} \]

   7. Taylor expanded in b around inf 39.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 19: 36.1% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.3e-12) (/ (/ x y) a) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e-12) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.3d-12) then
        tmp = (x / y) / a
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e-12) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.3e-12:
		tmp = (x / y) / a
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.3e-12)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.3e-12)
		tmp = (x / y) / a;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.3e-12], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.29999999999999989e-12

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 76.2%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 76.2%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 76.2%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 49.9%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 50.5%

         \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)}}{\frac{y}{x}}} \]

      2. +-commutative 50.5%

         \[\leadsto \frac{e^{-\color{blue}{\left(\log a + b\right)}}}{\frac{y}{x}} \]

      3. distribute-neg-in 50.5%

         \[\leadsto \frac{e^{\color{blue}{\left(-\log a\right) + \left(-b\right)}}}{\frac{y}{x}} \]

      4. neg-mul-1 50.5%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a} + \left(-b\right)}}{\frac{y}{x}} \]

      5. sub-neg 50.5%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a - b}}}{\frac{y}{x}} \]

      6. associate-/l* 49.9%

         \[\leadsto \color{blue}{\frac{e^{-1 \cdot \log a - b} \cdot x}{y}} \]

      7. *-commutative 49.9%

         \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]

      8. exp-diff 49.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}}}{y} \]

      9. neg-mul-1 49.9%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{-\log a}}}{e^{b}}}{y} \]

      10. associate-*r/ 47.3%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{-\log a}}{e^{b}}}}{y} \]

      11. log-rec 47.3%

          \[\leadsto \frac{\frac{x \cdot e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}}}{y} \]

      12. rem-exp-log 47.8%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

      13. associate-*r/ 47.8%

          \[\leadsto \frac{\frac{\color{blue}{\frac{x \cdot 1}{a}}}{e^{b}}}{y} \]

      14. *-rgt-identity 47.8%

          \[\leadsto \frac{\frac{\frac{\color{blue}{x}}{a}}{e^{b}}}{y} \]

      15. associate-/r* 47.8%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      16. *-commutative 47.8%

          \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

   7. Simplified 49.2%

      \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   8. Taylor expanded in b around 0 33.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if 2.29999999999999989e-12 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 91.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 91.9%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 91.9%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 71.0%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 71.0%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 71.0%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 71.0%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 71.0%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 56.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 56.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 56.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 56.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 66.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 74.6%

      \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   6. Taylor expanded in b around 0 39.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b + y\right)}} \]

   7. Taylor expanded in b around -inf 39.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 20: 31.1% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.35e-94) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.35e-94) {
		tmp = x / (y * a);
	} 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 (t <= 1.35d-94) then
        tmp = x / (y * a)
    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 (t <= 1.35e-94) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.35e-94:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.35e-94)
		tmp = Float64(x / Float64(y * a));
	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 (t <= 1.35e-94)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.35e-94], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.3500000000000001e-94

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.8%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.8%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 77.9%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 77.9%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 78.6%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 78.6%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 78.6%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 71.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 71.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 71.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 75.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 63.2%

      \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   6. Taylor expanded in b around 0 37.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 37.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   8. Simplified 37.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if 1.3500000000000001e-94 < t

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}{y}} \]

   3. Taylor expanded in b around 0 73.3%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

   4. Taylor expanded in t around 0 21.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 21: 32.5% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.08 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.08e-119) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.08e-119) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.08d-119) then
        tmp = (x / y) / a
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.08e-119) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.08e-119:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.08e-119)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.08e-119)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.08e-119], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.0799999999999999e-119

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 82.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 48.1%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 50.1%

         \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)}}{\frac{y}{x}}} \]

      2. +-commutative 50.1%

         \[\leadsto \frac{e^{-\color{blue}{\left(\log a + b\right)}}}{\frac{y}{x}} \]

      3. distribute-neg-in 50.1%

         \[\leadsto \frac{e^{\color{blue}{\left(-\log a\right) + \left(-b\right)}}}{\frac{y}{x}} \]

      4. neg-mul-1 50.1%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a} + \left(-b\right)}}{\frac{y}{x}} \]

      5. sub-neg 50.1%

         \[\leadsto \frac{e^{\color{blue}{-1 \cdot \log a - b}}}{\frac{y}{x}} \]

      6. associate-/l* 48.1%

         \[\leadsto \color{blue}{\frac{e^{-1 \cdot \log a - b} \cdot x}{y}} \]

      7. *-commutative 48.1%

         \[\leadsto \frac{\color{blue}{x \cdot e^{-1 \cdot \log a - b}}}{y} \]

      8. exp-diff 48.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{-1 \cdot \log a}}{e^{b}}}}{y} \]

      9. neg-mul-1 48.1%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{-\log a}}}{e^{b}}}{y} \]

      10. associate-*r/ 43.2%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{-\log a}}{e^{b}}}}{y} \]

      11. log-rec 43.2%

          \[\leadsto \frac{\frac{x \cdot e^{\color{blue}{\log \left(\frac{1}{a}\right)}}}{e^{b}}}{y} \]

      12. rem-exp-log 43.4%

          \[\leadsto \frac{\frac{x \cdot \color{blue}{\frac{1}{a}}}{e^{b}}}{y} \]

      13. associate-*r/ 43.4%

          \[\leadsto \frac{\frac{\color{blue}{\frac{x \cdot 1}{a}}}{e^{b}}}{y} \]

      14. *-rgt-identity 43.4%

          \[\leadsto \frac{\frac{\frac{\color{blue}{x}}{a}}{e^{b}}}{y} \]

      15. associate-/r* 43.4%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      16. *-commutative 43.4%

          \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

   7. Simplified 48.0%

      \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{e^{b}}}{a}} \]

   8. Taylor expanded in b around 0 31.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{a} \]

   if 1.0799999999999999e-119 < a

   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/ 87.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 87.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 87.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 87.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 74.8%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 74.8%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 75.3%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 75.3%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 75.3%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 67.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 67.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 67.8%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 64.4%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 62.7%

      \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

   6. Taylor expanded in b around 0 34.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   7. Step-by-step derivation

      1. *-commutative 34.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.08 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 22: 31.1% 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 98.6%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 88.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. *-commutative 88.5%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. +-commutative 88.5%

      \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

   4. associate--l+ 88.5%

      \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

   5. exp-sum 74.8%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 74.8%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 75.3%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 75.3%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 75.3%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 66.7%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 66.7%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 66.7%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 66.7%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

4. Taylor expanded in t around 0 66.5%

   \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

5. Taylor expanded in y around 0 57.0%

   \[\leadsto \frac{\color{blue}{x}}{a \cdot \left(y \cdot e^{b}\right)} \]

6. Taylor expanded in b around 0 31.4%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
7. Step-by-step derivation

   1. *-commutative 31.4%

      \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

8. Simplified 31.4%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

9. Final simplification 31.4%

   \[\leadsto \frac{x}{y \cdot a} \]

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 2023274 
(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))