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

Percentage Accurate: 98.3% → 98.3%

Time: 26.2s

Alternatives: 23

Speedup: 1.0×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+67)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (if (<= (+ t -1.0) 4e+105)
     (* x (/ (exp (- (- (* y (log z)) (log a)) b)) y))
     (/ (* x (pow a (+ t -1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+67) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else if ((t + -1.0) <= 4e+105) {
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-5d+67)) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else if ((t + (-1.0d0)) <= 4d+105) then
        tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y)
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+67) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else if ((t + -1.0) <= 4e+105) {
		tmp = x * (Math.exp((((y * Math.log(z)) - Math.log(a)) - b)) / y);
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+67:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	elif (t + -1.0) <= 4e+105:
		tmp = x * (math.exp((((y * math.log(z)) - math.log(a)) - b)) / y)
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+67)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	elseif (Float64(t + -1.0) <= 4e+105)
		tmp = Float64(x * Float64(exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b)) / y));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+67)
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	elseif ((t + -1.0) <= 4e+105)
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+67], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+105], N[(x * N[(N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -4.99999999999999976e67

   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. *-commutative 100.0%

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

      2. associate-/l* 89.1%

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

      3. associate--l+ 89.1%

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

      4. fma-define 89.1%

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

      5. sub-neg 89.1%

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

      6. metadata-eval 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around 0 95.7%

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

   if -4.99999999999999976e67 < (-.f64 t 1) < 3.9999999999999998e105

   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. *-commutative 97.5%

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

      2. associate-/l* 89.2%

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

      3. associate--l+ 89.2%

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

      4. fma-define 89.2%

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

      5. sub-neg 89.2%

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

      6. metadata-eval 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around 0 95.6%

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

      1. associate-/l* 95.7%

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

      2. +-commutative 95.7%

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

      3. mul-1-neg 95.7%

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

      4. unsub-neg 95.7%

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

   7. Simplified 95.7%

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

   if 3.9999999999999998e105 < (-.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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.0%

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

      4. associate-/l* 78.0%

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

      5. *-commutative 78.0%

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

      6. exp-to-pow 78.0%

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

      7. exp-diff 75.6%

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

      8. *-commutative 75.6%

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

      9. exp-to-pow 75.6%

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

      10. sub-neg 75.6%

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

      11. metadata-eval 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. associate-/r* 92.7%

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

      2. exp-to-pow 92.7%

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

      3. sub-neg 92.7%

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

      4. metadata-eval 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in b around 0 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+55)
   (/ (* x (pow a t)) (* y a))
   (if (<= (+ t -1.0) 2e+79)
     (/ (* x (pow z y)) (* a (* y (exp b))))
     (/ (* x (pow a (+ t -1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 2e+79) {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-5d+55)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t + (-1.0d0)) <= 2d+79) then
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 2e+79) {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+55:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t + -1.0) <= 2e+79:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+55)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t + -1.0) <= 2e+79)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+55)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t + -1.0) <= 2e+79)
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+55], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+79], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -5.00000000000000046e55

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 76.5%

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

      4. associate-/l* 76.5%

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

      5. *-commutative 76.5%

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

      6. exp-to-pow 76.5%

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

      7. exp-diff 70.6%

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

      8. *-commutative 70.6%

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

      9. exp-to-pow 70.6%

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

      10. sub-neg 70.6%

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

      11. metadata-eval 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 82.4%

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

      1. associate-/r* 82.4%

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

      2. exp-to-pow 82.4%

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

      3. sub-neg 82.4%

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

      4. metadata-eval 82.4%

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

   7. Simplified 82.4%

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

      1. unpow-prod-up 82.4%

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

      2. unpow-1 82.4%

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

   9. Applied egg-rr 82.4%

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

       1. associate-*r/ 82.4%

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

       2. *-rgt-identity 82.4%

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

   11. Simplified 82.4%

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

   12. Taylor expanded in b around 0 92.3%

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

   if -5.00000000000000046e55 < (-.f64 t 1) < 1.99999999999999993e79

   1. Initial program 97.3%

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

      1. associate-/l* 97.9%

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

      2. associate--l+ 97.9%

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

      3. exp-sum 82.9%

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

      4. associate-/l* 81.0%

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

      5. *-commutative 81.0%

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

      6. exp-to-pow 81.0%

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

      7. exp-diff 76.7%

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

      8. *-commutative 76.7%

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

      9. exp-to-pow 77.4%

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

      10. sub-neg 77.4%

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

      11. metadata-eval 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in t around 0 82.5%

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

   if 1.99999999999999993e79 < (-.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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 73.3%

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

      4. associate-/l* 73.3%

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

      5. *-commutative 73.3%

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

      6. exp-to-pow 73.3%

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

      7. exp-diff 71.1%

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

      8. *-commutative 71.1%

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

      9. exp-to-pow 71.1%

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

      10. sub-neg 71.1%

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

      11. metadata-eval 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 89.0%

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

      1. associate-/r* 89.0%

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

      2. exp-to-pow 89.0%

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

      3. sub-neg 89.0%

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

      4. metadata-eval 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in b around 0 93.4%

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

   10. Simplified 93.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+80} \lor \neg \left(b \leq 0.95\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.8e+80) (not (<= b 0.95)))
   (/ x (* y (exp b)))
   (* x (* (pow a (+ t -1.0)) (/ (pow z y) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.8e+80) || !(b <= 0.95)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x * (pow(a, (t + -1.0)) * (pow(z, y) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.8d+80)) .or. (.not. (b <= 0.95d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = x * ((a ** (t + (-1.0d0))) * ((z ** y) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.8e+80) || !(b <= 0.95)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) * (Math.pow(z, y) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.8e+80) or not (b <= 0.95):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x * (math.pow(a, (t + -1.0)) * (math.pow(z, y) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.8e+80) || !(b <= 0.95))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) * Float64((z ^ y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.8e+80) || ~((b <= 0.95)))
		tmp = x / (y * exp(b));
	else
		tmp = x * ((a ^ (t + -1.0)) * ((z ^ y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.8e+80], N[Not[LessEqual[b, 0.95]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.79999999999999984e80 or 0.94999999999999996 < 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. *-commutative 100.0%

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

      2. associate-/l* 89.8%

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

      3. associate--l+ 89.8%

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

      4. fma-define 89.8%

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

      5. sub-neg 89.8%

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

      6. metadata-eval 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in b around inf 77.1%

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

      1. neg-mul-1 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in b around inf 84.5%

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

      1. associate-*l/ 77.1%

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

      2. exp-neg 77.1%

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

      3. times-frac 84.5%

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

      4. *-rgt-identity 84.5%

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

   10. Simplified 84.5%

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

   if -6.79999999999999984e80 < b < 0.94999999999999996

   1. Initial program 97.1%

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

      1. associate-/l* 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 86.9%

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

      4. associate-/l* 84.9%

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

      5. *-commutative 84.9%

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

      6. exp-to-pow 84.9%

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

      7. exp-diff 84.2%

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

      8. *-commutative 84.2%

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

      9. exp-to-pow 85.1%

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

      10. sub-neg 85.1%

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

      11. metadata-eval 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in b around 0 87.0%

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

      1. associate-/l* 87.0%

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

      2. exp-to-pow 87.8%

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

      3. sub-neg 87.8%

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

      4. metadata-eval 87.8%

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

   7. Simplified 87.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+80} \lor \neg \left(b \leq 0.95\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16} \lor \neg \left(y \leq 2.6 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e+16) (not (<= y 2.6e+95)))
   (* 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 <= -8e+16) || !(y <= 2.6e+95)) {
		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 <= (-8d+16)) .or. (.not. (y <= 2.6d+95))) 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 <= -8e+16) || !(y <= 2.6e+95)) {
		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 <= -8e+16) or not (y <= 2.6e+95):
		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 <= -8e+16) || !(y <= 2.6e+95))
		tmp = Float64(x * Float64(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 <= -8e+16) || ~((y <= 2.6e+95)))
		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, -8e+16], N[Not[LessEqual[y, 2.6e+95]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $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 < -8e16 or 2.5999999999999999e95 < 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. *-commutative 100.0%

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

      2. associate-/l* 87.1%

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

      3. associate--l+ 87.1%

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

      4. fma-define 87.1%

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

      5. sub-neg 87.1%

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

      6. metadata-eval 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around 0 91.2%

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

      1. associate-/l* 91.2%

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

      2. +-commutative 91.2%

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

      3. mul-1-neg 91.2%

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

      4. unsub-neg 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in b around 0 81.5%

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

      1. div-exp 81.5%

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

      2. *-commutative 81.5%

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

      3. exp-to-pow 81.5%

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

      4. rem-exp-log 81.5%

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

   10. Simplified 81.5%

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

   if -8e16 < y < 2.5999999999999999e95

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-/l* 90.8%

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

      3. associate--l+ 90.8%

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

      4. fma-define 90.8%

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

      5. sub-neg 90.8%

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

      6. metadata-eval 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 95.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16} \lor \neg \left(y \leq 2.6 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 0.95:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e+79)
   (* (exp (- (* (+ t -1.0) (log a)) b)) (/ x y))
   (if (<= b 0.95)
     (* x (* (pow a (+ t -1.0)) (/ (pow z y) y)))
     (/ x (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+79) {
		tmp = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	} else if (b <= 0.95) {
		tmp = x * (pow(a, (t + -1.0)) * (pow(z, y) / y));
	} else {
		tmp = 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 (b <= (-1.05d+79)) then
        tmp = exp((((t + (-1.0d0)) * log(a)) - b)) * (x / y)
    else if (b <= 0.95d0) then
        tmp = x * ((a ** (t + (-1.0d0))) * ((z ** y) / y))
    else
        tmp = 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 (b <= -1.05e+79) {
		tmp = Math.exp((((t + -1.0) * Math.log(a)) - b)) * (x / y);
	} else if (b <= 0.95) {
		tmp = x * (Math.pow(a, (t + -1.0)) * (Math.pow(z, y) / y));
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e+79:
		tmp = math.exp((((t + -1.0) * math.log(a)) - b)) * (x / y)
	elif b <= 0.95:
		tmp = x * (math.pow(a, (t + -1.0)) * (math.pow(z, y) / y))
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e+79)
		tmp = Float64(exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b)) * Float64(x / y));
	elseif (b <= 0.95)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) * Float64((z ^ y) / y)));
	else
		tmp = 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 (b <= -1.05e+79)
		tmp = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	elseif (b <= 0.95)
		tmp = x * ((a ^ (t + -1.0)) * ((z ^ y) / y));
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e+79], N[(N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.95], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05000000000000004e79

   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. *-commutative 100.0%

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

      2. associate-/l* 94.0%

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

      3. associate--l+ 94.0%

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

      4. fma-define 94.0%

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

      5. sub-neg 94.0%

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

      6. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around 0 84.1%

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

   if -1.05000000000000004e79 < b < 0.94999999999999996

   1. Initial program 97.1%

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

      1. associate-/l* 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 86.9%

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

      4. associate-/l* 84.9%

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

      5. *-commutative 84.9%

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

      6. exp-to-pow 84.9%

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

      7. exp-diff 84.2%

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

      8. *-commutative 84.2%

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

      9. exp-to-pow 85.1%

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

      10. sub-neg 85.1%

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

      11. metadata-eval 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in b around 0 87.0%

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

      1. associate-/l* 87.0%

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

      2. exp-to-pow 87.8%

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

      3. sub-neg 87.8%

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

      4. metadata-eval 87.8%

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

   7. Simplified 87.8%

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

   if 0.94999999999999996 < 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. *-commutative 100.0%

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

      2. associate-/l* 86.2%

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

      3. associate--l+ 86.2%

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

      4. fma-define 86.2%

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

      5. sub-neg 86.2%

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

      6. metadata-eval 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in b around inf 77.8%

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

      1. neg-mul-1 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in b around inf 86.4%

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

      1. associate-*l/ 77.8%

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

      2. exp-neg 77.8%

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

      3. times-frac 86.4%

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

      4. *-rgt-identity 86.4%

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

   10. Simplified 86.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 0.95:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+16} \lor \neg \left(y \leq 5.2 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e+16) (not (<= y 5.2e+94)))
   (* x (/ (/ (pow z y) a) y))
   (* x (/ (/ (/ (pow a t) a) y) (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+16) || !(y <= 5.2e+94)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = x * (((pow(a, t) / a) / y) / exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.5d+16)) .or. (.not. (y <= 5.2d+94))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = x * ((((a ** t) / a) / y) / exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+16) || !(y <= 5.2e+94)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = x * (((Math.pow(a, t) / a) / y) / Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e+16) or not (y <= 5.2e+94):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = x * (((math.pow(a, t) / a) / y) / math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e+16) || !(y <= 5.2e+94))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(x * Float64(Float64(Float64((a ^ t) / a) / y) / exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e+16) || ~((y <= 5.2e+94)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = x * ((((a ^ t) / a) / y) / exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e+16], N[Not[LessEqual[y, 5.2e+94]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e16 or 5.1999999999999998e94 < 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. *-commutative 100.0%

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

      2. associate-/l* 87.3%

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

      3. associate--l+ 87.3%

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

      4. fma-define 87.3%

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

      5. sub-neg 87.3%

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

      6. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in t around 0 91.3%

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

      1. associate-/l* 91.3%

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

      2. +-commutative 91.3%

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

      3. mul-1-neg 91.3%

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

      4. unsub-neg 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in b around 0 80.7%

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

      1. div-exp 80.7%

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

      2. *-commutative 80.7%

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

      3. exp-to-pow 80.7%

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

      4. rem-exp-log 80.7%

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

   10. Simplified 80.7%

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

   if -9.5e16 < y < 5.1999999999999998e94

   1. Initial program 97.2%

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

      1. associate-/l* 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 92.0%

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

      4. associate-/l* 92.0%

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

      5. *-commutative 92.0%

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

      6. exp-to-pow 92.0%

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

      7. exp-diff 86.8%

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

      8. *-commutative 86.8%

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

      9. exp-to-pow 87.6%

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

      10. sub-neg 87.6%

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

      11. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 90.8%

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

      1. associate-/r* 88.2%

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

      2. exp-to-pow 89.0%

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

      3. sub-neg 89.0%

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

      4. metadata-eval 89.0%

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

   7. Simplified 89.0%

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

      1. unpow-prod-up 89.1%

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

      2. unpow-1 89.1%

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

   9. Applied egg-rr 89.1%

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

       1. associate-*r/ 89.1%

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

       2. *-rgt-identity 89.1%

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

   11. Simplified 89.1%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+16} \lor \neg \left(y \leq 5.2 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-257}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 0.95:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -1.3e+48)
     t_1
     (if (<= b 1.9e-257)
       (* (pow a (+ t -1.0)) (/ x y))
       (if (<= b 0.95) (* x (/ (/ (pow z y) a) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double tmp;
	if (b <= -1.3e+48) {
		tmp = t_1;
	} else if (b <= 1.9e-257) {
		tmp = pow(a, (t + -1.0)) * (x / y);
	} else if (b <= 0.95) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * exp(b))
    if (b <= (-1.3d+48)) then
        tmp = t_1
    else if (b <= 1.9d-257) then
        tmp = (a ** (t + (-1.0d0))) * (x / y)
    else if (b <= 0.95d0) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -1.3e+48) {
		tmp = t_1;
	} else if (b <= 1.9e-257) {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	} else if (b <= 0.95) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	tmp = 0
	if b <= -1.3e+48:
		tmp = t_1
	elif b <= 1.9e-257:
		tmp = math.pow(a, (t + -1.0)) * (x / y)
	elif b <= 0.95:
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -1.3e+48)
		tmp = t_1;
	elseif (b <= 1.9e-257)
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / y));
	elseif (b <= 0.95)
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -1.3e+48)
		tmp = t_1;
	elseif (b <= 1.9e-257)
		tmp = (a ^ (t + -1.0)) * (x / y);
	elseif (b <= 0.95)
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+48], t$95$1, If[LessEqual[b, 1.9e-257], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.95], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.29999999999999998e48 or 0.94999999999999996 < 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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 87.8%

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

      4. fma-define 87.8%

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

      5. sub-neg 87.8%

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

      6. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in b around inf 74.1%

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

      1. neg-mul-1 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in b around inf 83.7%

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

      1. associate-*l/ 74.1%

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

      2. exp-neg 74.1%

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

      3. times-frac 83.7%

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

      4. *-rgt-identity 83.7%

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

   10. Simplified 83.7%

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

   if -1.29999999999999998e48 < b < 1.9000000000000002e-257

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-/l* 96.5%

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

      3. associate--l+ 96.5%

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

      4. fma-define 96.5%

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

      5. sub-neg 96.5%

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

      6. metadata-eval 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 80.9%

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

   6. Taylor expanded in b around 0 78.5%

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

      1. exp-to-pow 79.2%

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

      2. sub-neg 79.2%

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

      3. metadata-eval 79.2%

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

      4. +-commutative 79.2%

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

   8. Simplified 79.2%

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

   if 1.9000000000000002e-257 < b < 0.94999999999999996

   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. *-commutative 98.5%

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

      2. associate-/l* 82.9%

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

      3. associate--l+ 82.9%

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

      4. fma-define 82.9%

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

      5. sub-neg 82.9%

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

      6. metadata-eval 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in t around 0 78.9%

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

      1. associate-/l* 77.6%

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

      2. +-commutative 77.6%

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

      3. mul-1-neg 77.6%

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

      4. unsub-neg 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in b around 0 77.6%

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

      1. div-exp 77.6%

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

      2. *-commutative 77.6%

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

      3. exp-to-pow 77.6%

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

      4. rem-exp-log 78.7%

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

   10. Simplified 78.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-257}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 0.95:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -5e+55)
   (/ (* x (pow a t)) (* y a))
   (if (<= (+ t -1.0) 4e+105)
     (/ x (* a (* y (exp b))))
     (/ (* x (pow a (+ t -1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 4e+105) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-5d+55)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t + (-1.0d0)) <= 4d+105) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t + -1.0) <= 4e+105) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -5e+55:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t + -1.0) <= 4e+105:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+55)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t + -1.0) <= 4e+105)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -5e+55)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t + -1.0) <= 4e+105)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+55], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+105], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -5.00000000000000046e55

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 76.5%

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

      4. associate-/l* 76.5%

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

      5. *-commutative 76.5%

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

      6. exp-to-pow 76.5%

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

      7. exp-diff 70.6%

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

      8. *-commutative 70.6%

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

      9. exp-to-pow 70.6%

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

      10. sub-neg 70.6%

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

      11. metadata-eval 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around 0 82.4%

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

      1. associate-/r* 82.4%

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

      2. exp-to-pow 82.4%

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

      3. sub-neg 82.4%

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

      4. metadata-eval 82.4%

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

   7. Simplified 82.4%

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

      1. unpow-prod-up 82.4%

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

      2. unpow-1 82.4%

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

   9. Applied egg-rr 82.4%

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

       1. associate-*r/ 82.4%

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

       2. *-rgt-identity 82.4%

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

   11. Simplified 82.4%

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

   12. Taylor expanded in b around 0 92.3%

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

   if -5.00000000000000046e55 < (-.f64 t 1) < 3.9999999999999998e105

   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. *-commutative 97.4%

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

      2. associate-/l* 88.9%

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

      3. associate--l+ 88.9%

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

      4. fma-define 88.9%

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

      5. sub-neg 88.9%

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

      6. metadata-eval 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 95.5%

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

      1. associate-/l* 95.6%

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

      2. +-commutative 95.6%

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

      3. mul-1-neg 95.6%

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

      4. unsub-neg 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in y around 0 70.7%

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

      1. exp-neg 70.7%

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

      2. associate-*r/ 70.7%

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

      3. *-rgt-identity 70.7%

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

      4. +-commutative 70.7%

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

      5. exp-sum 70.7%

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

      6. rem-exp-log 71.5%

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

      7. associate-/r* 66.0%

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

      8. associate-/r* 66.0%

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

      9. *-commutative 66.0%

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

      10. associate-/r* 72.1%

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

   10. Simplified 72.1%

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

   if 3.9999999999999998e105 < (-.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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.0%

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

      4. associate-/l* 78.0%

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

      5. *-commutative 78.0%

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

      6. exp-to-pow 78.0%

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

      7. exp-diff 75.6%

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

      8. *-commutative 75.6%

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

      9. exp-to-pow 75.6%

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

      10. sub-neg 75.6%

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

      11. metadata-eval 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. associate-/r* 92.7%

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

      2. exp-to-pow 92.7%

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

      3. sub-neg 92.7%

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

      4. metadata-eval 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in b around 0 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -780 \lor \neg \left(b \leq 0.95\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -780.0) (not (<= b 0.95)))
   (/ x (* y (exp b)))
   (* x (/ (/ (pow z y) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -780.0) || !(b <= 0.95)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x * ((pow(z, y) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-780.0d0)) .or. (.not. (b <= 0.95d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = x * (((z ** y) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -780.0) || !(b <= 0.95)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -780.0) or not (b <= 0.95):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -780.0) || !(b <= 0.95))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -780.0) || ~((b <= 0.95)))
		tmp = x / (y * exp(b));
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -780.0], N[Not[LessEqual[b, 0.95]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -780 or 0.94999999999999996 < 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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 88.6%

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

      4. fma-define 88.6%

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

      5. sub-neg 88.6%

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

      6. metadata-eval 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in b around inf 74.2%

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

      1. neg-mul-1 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in b around inf 83.2%

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

      1. associate-*l/ 74.2%

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

      2. exp-neg 74.2%

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

      3. times-frac 83.2%

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

      4. *-rgt-identity 83.2%

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

   10. Simplified 83.2%

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

   if -780 < b < 0.94999999999999996

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-/l* 90.1%

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

      3. associate--l+ 90.1%

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

      4. fma-define 90.1%

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

      5. sub-neg 90.1%

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

      6. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in t around 0 69.5%

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

      1. associate-/l* 70.4%

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

      2. +-commutative 70.4%

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

      3. mul-1-neg 70.4%

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

      4. unsub-neg 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in b around 0 70.4%

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

      1. div-exp 70.4%

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

      2. *-commutative 70.4%

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

      3. exp-to-pow 70.4%

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

      4. rem-exp-log 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -780 \lor \neg \left(b \leq 0.95\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+217} \lor \neg \left(y \leq -1.06 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e+217) (not (<= y -1.06e+136)))
   (/ x (* a (* y (exp b))))
   (* x (/ (exp b) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+217) || !(y <= -1.06e+136)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (exp(b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4d+217)) .or. (.not. (y <= (-1.06d+136)))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (exp(b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+217) || !(y <= -1.06e+136)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.exp(b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e+217) or not (y <= -1.06e+136):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.exp(b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e+217) || !(y <= -1.06e+136))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(exp(b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4e+217) || ~((y <= -1.06e+136)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (exp(b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e+217], N[Not[LessEqual[y, -1.06e+136]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999984e217 or -1.06000000000000003e136 < y

   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. *-commutative 98.2%

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

      2. associate-/l* 88.9%

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

      3. associate--l+ 88.9%

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

      4. fma-define 88.9%

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

      5. sub-neg 88.9%

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

      6. metadata-eval 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around 0 81.6%

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

      1. associate-/l* 82.1%

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

      2. +-commutative 82.1%

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

      3. mul-1-neg 82.1%

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

      4. unsub-neg 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in y around 0 63.9%

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

      1. exp-neg 63.9%

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

      2. associate-*r/ 63.9%

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

      3. *-rgt-identity 63.9%

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

      4. +-commutative 63.9%

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

      5. exp-sum 63.9%

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

      6. rem-exp-log 64.5%

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

      7. associate-/r* 59.8%

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

      8. associate-/r* 59.8%

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

      9. *-commutative 59.8%

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

      10. associate-/r* 65.7%

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

   10. Simplified 65.7%

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

   if -3.99999999999999984e217 < y < -1.06000000000000003e136

   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. *-commutative 100.0%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-define 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 26.6%

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

      1. neg-mul-1 26.6%

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

   7. Simplified 26.6%

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

   8. Taylor expanded in b around inf 26.6%

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

      1. associate-*r/ 26.6%

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

   10. Simplified 26.6%

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

       1. associate-*r/ 26.6%

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

       2. add-sqr-sqrt 10.7%

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

       3. sqrt-unprod 41.4%

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

       4. sqr-neg 41.4%

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

       5. sqrt-unprod 30.7%

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

       6. add-sqr-sqrt 70.9%

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

   12. Applied egg-rr 70.9%

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

       1. associate-*r/ 70.9%

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

   14. Simplified 70.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+217} \lor \neg \left(y \leq -1.06 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19} \lor \neg \left(b \leq 0.0005\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.2e-19) (not (<= b 0.0005)))
   (/ x (* y (exp b)))
   (/ x (* y (+ a (* b (+ a (* 0.5 (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.2e-19) || !(b <= 0.0005)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (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 <= (-7.2d-19)) .or. (.not. (b <= 0.0005d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = x / (y * (a + (b * (a + (0.5d0 * (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 <= -7.2e-19) || !(b <= 0.0005)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.2e-19) or not (b <= 0.0005):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.2e-19) || !(b <= 0.0005))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.2e-19) || ~((b <= 0.0005)))
		tmp = x / (y * exp(b));
	else
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.2e-19], N[Not[LessEqual[b, 0.0005]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e-19 or 5.0000000000000001e-4 < 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. *-commutative 100.0%

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

      2. associate-/l* 89.1%

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

      3. associate--l+ 89.1%

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

      4. fma-define 89.1%

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

      5. sub-neg 89.1%

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

      6. metadata-eval 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in b around inf 72.4%

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

      1. neg-mul-1 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in b around inf 81.0%

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

      1. associate-*l/ 72.4%

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

      2. exp-neg 72.4%

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

      3. times-frac 81.0%

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

      4. *-rgt-identity 81.0%

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

   10. Simplified 81.0%

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

   if -7.2000000000000002e-19 < b < 5.0000000000000001e-4

   1. Initial program 96.6%

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

      1. associate-/l* 97.4%

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

      2. associate--l+ 97.4%

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

      3. exp-sum 87.9%

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

      4. associate-/l* 86.4%

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

      5. *-commutative 86.4%

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

      6. exp-to-pow 86.4%

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

      7. exp-diff 86.4%

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

      8. *-commutative 86.4%

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

      9. exp-to-pow 87.3%

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

      10. sub-neg 87.3%

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

      11. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around 0 76.8%

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

      1. associate-/r* 76.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   7. Simplified 77.8%

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

      1. unpow-prod-up 77.9%

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

      2. unpow-1 77.9%

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

   9. Applied egg-rr 77.9%

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

       1. associate-*r/ 77.9%

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

       2. *-rgt-identity 77.9%

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

   11. Simplified 77.9%

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

   12. Taylor expanded in t around 0 44.1%

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

       1. associate-*r* 44.1%

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

       2. *-commutative 44.1%

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

       3. associate-*l* 44.1%

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

   14. Simplified 44.1%

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

   15. Taylor expanded in b around 0 44.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19} \lor \neg \left(b \leq 0.0005\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.7% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) + \frac{-1}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e-19)
   (*
    x
    (+
     (/ 1.0 y)
     (*
      b
      (+
       (* b (+ (* -0.16666666666666666 (/ b y)) (* 0.5 (/ 1.0 y))))
       (/ -1.0 y)))))
   (/
    x
    (*
     y
     (+ a (* b (+ a (* b (+ (* (* a b) 0.16666666666666666) (* a 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))));
	} else {
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.2d-19)) then
        tmp = x * ((1.0d0 / y) + (b * ((b * (((-0.16666666666666666d0) * (b / y)) + (0.5d0 * (1.0d0 / y)))) + ((-1.0d0) / y))))
    else
        tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666d0) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))));
	} else {
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e-19:
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))))
	else:
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e-19)
		tmp = Float64(x * Float64(Float64(1.0 / y) + Float64(b * Float64(Float64(b * Float64(Float64(-0.16666666666666666 * Float64(b / y)) + Float64(0.5 * Float64(1.0 / y)))) + Float64(-1.0 / y)))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(Float64(a * b) * 0.16666666666666666) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.2e-19)
		tmp = x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))));
	else
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e-19], N[(x * N[(N[(1.0 / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(-0.16666666666666666 * N[(b / y), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(N[(a * b), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e-19

   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. *-commutative 100.0%

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

      2. associate-/l* 91.4%

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

      3. associate--l+ 91.4%

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

      4. fma-define 91.4%

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

      5. sub-neg 91.4%

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

      6. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in b around inf 68.9%

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

      1. neg-mul-1 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in b around 0 58.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   if -7.2000000000000002e-19 < b

   1. Initial program 97.7%

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

      1. associate-/l* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 83.7%

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

      4. associate-/l* 82.6%

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

      5. *-commutative 82.6%

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

      6. exp-to-pow 82.6%

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

      7. exp-diff 81.5%

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

      8. *-commutative 81.5%

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

      9. exp-to-pow 82.2%

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

      10. sub-neg 82.2%

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

      11. metadata-eval 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in y around 0 77.2%

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

      1. associate-/r* 75.1%

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

      2. exp-to-pow 75.8%

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

      3. sub-neg 75.8%

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

      4. metadata-eval 75.8%

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

   7. Simplified 75.8%

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

      1. unpow-prod-up 75.8%

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

      2. unpow-1 75.8%

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

   9. Applied egg-rr 75.8%

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

       1. associate-*r/ 75.8%

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

       2. *-rgt-identity 75.8%

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

   11. Simplified 75.8%

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

   12. Taylor expanded in t around 0 57.1%

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

       1. associate-*r* 55.5%

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

       2. *-commutative 55.5%

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

       3. associate-*l* 57.1%

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

   14. Simplified 57.1%

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

   15. Taylor expanded in b around 0 53.0%

       \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) + \frac{-1}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.6% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{x + b \cdot \left(x \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.3e+120)
   (/ (+ x (* b (* x (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666))))))) y)
   (/
    x
    (*
     y
     (+ a (* b (+ a (* b (+ (* (* a b) 0.16666666666666666) (* a 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+120) {
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.3d+120)) then
        tmp = (x + (b * (x * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0)))))))) / y
    else
        tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666d0) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+120) {
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.3e+120:
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y
	else:
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.3e+120)
		tmp = Float64(Float64(x + Float64(b * Float64(x * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(Float64(a * b) * 0.16666666666666666) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.3e+120)
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	else
		tmp = x / (y * (a + (b * (a + (b * (((a * b) * 0.16666666666666666) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.3e+120], N[(N[(x + N[(b * N[(x * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(N[(a * b), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.29999999999999991e120

   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. *-commutative 100.0%

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

      2. associate-/l* 92.1%

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

      3. associate--l+ 92.1%

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

      4. fma-define 92.1%

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

      5. sub-neg 92.1%

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

      6. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in b around inf 84.3%

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

      1. neg-mul-1 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in b around 0 85.0%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 89.8%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in x around 0 92.2%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}}{y} \]

   if -3.29999999999999991e120 < b

   1. Initial program 98.0%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 82.0%

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

      4. associate-/l* 80.6%

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

      5. *-commutative 80.6%

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

      6. exp-to-pow 80.6%

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

      7. exp-diff 77.8%

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

      8. *-commutative 77.8%

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

      9. exp-to-pow 78.4%

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

      10. sub-neg 78.4%

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

      11. metadata-eval 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. associate-/r* 71.9%

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

      2. exp-to-pow 72.5%

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

      3. sub-neg 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. unpow-prod-up 72.6%

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

      2. unpow-1 72.6%

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

   9. Applied egg-rr 72.6%

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

       1. associate-*r/ 72.6%

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

       2. *-rgt-identity 72.6%

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

   11. Simplified 72.6%

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

   12. Taylor expanded in t around 0 57.1%

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

       1. associate-*r* 54.8%

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

       2. *-commutative 54.8%

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

       3. associate-*l* 57.1%

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

   14. Simplified 57.1%

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

   15. Taylor expanded in b around 0 49.5%

       \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{x + b \cdot \left(x \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(\left(a \cdot b\right) \cdot 0.16666666666666666 + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.0% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+120}:\\ \;\;\;\;\frac{x + b \cdot \left(x \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+120)
   (/ (+ x (* b (* x (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666))))))) y)
   (/ x (* y (+ a (* b (+ a (* 0.5 (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+120) {
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (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 <= (-2.9d+120)) then
        tmp = (x + (b * (x * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0)))))))) / y
    else
        tmp = x / (y * (a + (b * (a + (0.5d0 * (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 <= -2.9e+120) {
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e+120:
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y
	else:
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+120)
		tmp = Float64(Float64(x + Float64(b * Float64(x * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e+120)
		tmp = (x + (b * (x * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	else
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+120], N[(N[(x + N[(b * N[(x * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.9000000000000001e120

   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. *-commutative 100.0%

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

      2. associate-/l* 92.1%

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

      3. associate--l+ 92.1%

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

      4. fma-define 92.1%

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

      5. sub-neg 92.1%

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

      6. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in b around inf 84.3%

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

      1. neg-mul-1 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in b around 0 85.0%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 89.8%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in x around 0 92.2%

       \[\leadsto \frac{x + \color{blue}{b \cdot \left(x \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}}{y} \]

   if -2.9000000000000001e120 < b

   1. Initial program 98.0%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 82.0%

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

      4. associate-/l* 80.6%

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

      5. *-commutative 80.6%

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

      6. exp-to-pow 80.6%

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

      7. exp-diff 77.8%

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

      8. *-commutative 77.8%

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

      9. exp-to-pow 78.4%

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

      10. sub-neg 78.4%

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

      11. metadata-eval 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. associate-/r* 71.9%

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

      2. exp-to-pow 72.5%

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

      3. sub-neg 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. unpow-prod-up 72.6%

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

      2. unpow-1 72.6%

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

   9. Applied egg-rr 72.6%

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

       1. associate-*r/ 72.6%

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

       2. *-rgt-identity 72.6%

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

   11. Simplified 72.6%

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

   12. Taylor expanded in t around 0 57.1%

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

       1. associate-*r* 54.8%

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

       2. *-commutative 54.8%

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

       3. associate-*l* 57.1%

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

   14. Simplified 57.1%

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

   15. Taylor expanded in b around 0 47.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+120}:\\ \;\;\;\;\frac{x + b \cdot \left(x \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.6% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+120}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e+120)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y)
   (/ x (* y (+ a (* b (+ a (* 0.5 (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e+120) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (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 <= (-3d+120)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else
        tmp = x / (y * (a + (b * (a + (0.5d0 * (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 <= -3e+120) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e+120:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	else:
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e+120)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e+120)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	else
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e+120], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3e120

   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. *-commutative 100.0%

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

      2. associate-/l* 92.1%

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

      3. associate--l+ 92.1%

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

      4. fma-define 92.1%

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

      5. sub-neg 92.1%

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

      6. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in b around inf 84.3%

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

      1. neg-mul-1 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in b around inf 92.2%

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

      1. associate-*r/ 92.2%

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

   10. Simplified 92.2%

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

   11. Taylor expanded in b around 0 79.7%

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

   12. Taylor expanded in y around 0 84.9%

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

   if -3e120 < b

   1. Initial program 98.0%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 82.0%

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

      4. associate-/l* 80.6%

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

      5. *-commutative 80.6%

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

      6. exp-to-pow 80.6%

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

      7. exp-diff 77.8%

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

      8. *-commutative 77.8%

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

      9. exp-to-pow 78.4%

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

      10. sub-neg 78.4%

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

      11. metadata-eval 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. associate-/r* 71.9%

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

      2. exp-to-pow 72.5%

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

      3. sub-neg 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. unpow-prod-up 72.6%

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

      2. unpow-1 72.6%

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

   9. Applied egg-rr 72.6%

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

       1. associate-*r/ 72.6%

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

       2. *-rgt-identity 72.6%

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

   11. Simplified 72.6%

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

   12. Taylor expanded in t around 0 57.1%

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

       1. associate-*r* 54.8%

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

       2. *-commutative 54.8%

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

       3. associate-*l* 57.1%

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

   14. Simplified 57.1%

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

   15. Taylor expanded in b around 0 47.0%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+120}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \frac{0.5}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e-19)
   (* x (+ (/ 1.0 y) (* b (* b (/ 0.5 y)))))
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) + (b * (b * (0.5 / y))));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.2d-19)) then
        tmp = x * ((1.0d0 / y) + (b * (b * (0.5d0 / y))))
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) + (b * (b * (0.5 / y))));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e-19:
		tmp = x * ((1.0 / y) + (b * (b * (0.5 / y))))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e-19)
		tmp = Float64(x * Float64(Float64(1.0 / y) + Float64(b * Float64(b * Float64(0.5 / y)))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.2e-19)
		tmp = x * ((1.0 / y) + (b * (b * (0.5 / y))));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e-19], N[(x * N[(N[(1.0 / y), $MachinePrecision] + N[(b * N[(b * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e-19

   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. *-commutative 100.0%

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

      2. associate-/l* 91.4%

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

      3. associate--l+ 91.4%

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

      4. fma-define 91.4%

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

      5. sub-neg 91.4%

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

      6. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in b around inf 68.9%

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

      1. neg-mul-1 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in b around inf 77.6%

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

      1. associate-*r/ 77.6%

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

   10. Simplified 77.6%

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

   11. Taylor expanded in b around 0 57.1%

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

   12. Taylor expanded in b around inf 57.1%

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

       1. associate-*r/ 57.1%

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

       2. *-commutative 57.1%

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

       3. associate-/l* 57.1%

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

   14. Simplified 57.1%

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

   if -7.2000000000000002e-19 < b

   1. Initial program 97.7%

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

      1. associate-/l* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 83.7%

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

      4. associate-/l* 82.6%

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

      5. *-commutative 82.6%

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

      6. exp-to-pow 82.6%

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

      7. exp-diff 81.5%

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

      8. *-commutative 81.5%

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

      9. exp-to-pow 82.2%

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

      10. sub-neg 82.2%

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

      11. metadata-eval 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in y around 0 77.2%

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

      1. associate-/r* 75.1%

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

      2. exp-to-pow 75.8%

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

      3. sub-neg 75.8%

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

      4. metadata-eval 75.8%

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

   7. Simplified 75.8%

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

      1. unpow-prod-up 75.8%

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

      2. unpow-1 75.8%

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

   9. Applied egg-rr 75.8%

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

       1. associate-*r/ 75.8%

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

       2. *-rgt-identity 75.8%

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

   11. Simplified 75.8%

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

   12. Taylor expanded in t around 0 57.1%

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

       1. associate-*r* 55.5%

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

       2. *-commutative 55.5%

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

       3. associate-*l* 57.1%

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

   14. Simplified 57.1%

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

   15. Taylor expanded in b around 0 45.2%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \frac{0.5}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.0% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.7e+106) (* x (- (/ 1.0 y) (/ b y))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.7e+106) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.7d+106)) then
        tmp = x * ((1.0d0 / y) - (b / y))
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.7e+106) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.7e+106:
		tmp = x * ((1.0 / y) - (b / y))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.7e+106)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b / y)));
	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 (b <= -6.7e+106)
		tmp = x * ((1.0 / y) - (b / y));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.7e+106], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.7e106

   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. *-commutative 100.0%

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

      2. associate-/l* 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. associate--l+ 93.2%

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

      4. fma-define 93.2%

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

      5. sub-neg 93.2%

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

      6. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in b around inf 77.5%

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

      1. neg-mul-1 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in b around inf 84.3%

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

      1. associate-*r/ 84.3%

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

   10. Simplified 84.3%

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

   11. Taylor expanded in b around 0 58.4%

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

       1. +-commutative 58.4%

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

       2. mul-1-neg 58.4%

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

       3. unsub-neg 58.4%

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

   13. Simplified 58.4%

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

   if -6.7e106 < b

   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. *-commutative 98.0%

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

      2. associate-/l* 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. associate--l+ 88.6%

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

      4. fma-define 88.6%

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

      5. sub-neg 88.6%

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

      6. metadata-eval 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in y around 0 71.2%

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

   6. Taylor expanded in b around 0 57.6%

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

      1. exp-to-pow 58.2%

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

      2. sub-neg 58.2%

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

      3. metadata-eval 58.2%

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

      4. +-commutative 58.2%

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

   8. Simplified 58.2%

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

   9. Taylor expanded in t around 0 37.2%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.5% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e-19) (* x (- (/ 1.0 y) (/ b y))) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) - (b / y));
	} 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 <= (-7.2d-19)) then
        tmp = x * ((1.0d0 / y) - (b / y))
    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 <= -7.2e-19) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e-19:
		tmp = x * ((1.0 / y) - (b / y))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e-19)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b / y)));
	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 <= -7.2e-19)
		tmp = x * ((1.0 / y) - (b / y));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e-19], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e-19

   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. *-commutative 100.0%

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

      2. associate-/l* 91.4%

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

      3. associate--l+ 91.4%

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

      4. fma-define 91.4%

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

      5. sub-neg 91.4%

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

      6. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in b around inf 68.9%

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

      1. neg-mul-1 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in b around inf 77.6%

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

      1. associate-*r/ 77.6%

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

   10. Simplified 77.6%

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

   11. Taylor expanded in b around 0 44.8%

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

       1. +-commutative 44.8%

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

       2. mul-1-neg 44.8%

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

       3. unsub-neg 44.8%

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

   13. Simplified 44.8%

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

   if -7.2000000000000002e-19 < b

   1. Initial program 97.7%

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

      1. associate-/l* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 83.7%

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

      4. associate-/l* 82.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 75.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 75.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 75.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 75.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 75.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 75.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y}}{e^{b}} \]

      2. unpow-1 75.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y}}{e^{b}} \]

   9. Applied egg-rr 75.8%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y}}{e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.8%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y}}{e^{b}} \]

       2. *-rgt-identity 75.8%

          \[\leadsto x \cdot \frac{\frac{\frac{\color{blue}{{a}^{t}}}{a}}{y}}{e^{b}} \]

   11. Simplified 75.8%

       \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t}}{a}}}{y}}{e^{b}} \]

   12. Taylor expanded in t around 0 57.1%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 55.5%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

       2. *-commutative 55.5%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

       3. associate-*l* 57.1%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   14. Simplified 57.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   15. Taylor expanded in b around 0 42.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   16. Step-by-step derivation

       1. distribute-lft-out 44.7%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 44.7%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   17. Simplified 44.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.0% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e-19) (* x (- (/ 1.0 y) (/ b y))) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.2d-19)) then
        tmp = x * ((1.0d0 / y) - (b / y))
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e-19) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e-19:
		tmp = x * ((1.0 / y) - (b / y))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e-19)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b / y)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.2e-19)
		tmp = x * ((1.0 / y) - (b / y));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e-19], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e-19

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 91.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 91.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 91.4%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 91.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 91.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 68.9%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 68.9%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 68.9%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around inf 77.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{-b}}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 77.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{-b}}{y}} \]

   10. Simplified 77.6%

       \[\leadsto \color{blue}{x \cdot \frac{e^{-b}}{y}} \]

   11. Taylor expanded in b around 0 44.8%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{y} + \frac{1}{y}\right)} \]
   12. Step-by-step derivation

       1. +-commutative 44.8%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} + -1 \cdot \frac{b}{y}\right)} \]

       2. mul-1-neg 44.8%

          \[\leadsto x \cdot \left(\frac{1}{y} + \color{blue}{\left(-\frac{b}{y}\right)}\right) \]

       3. unsub-neg 44.8%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   13. Simplified 44.8%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   if -7.2000000000000002e-19 < b

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 75.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 75.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 75.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 75.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 75.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 75.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y}}{e^{b}} \]

      2. unpow-1 75.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y}}{e^{b}} \]

   9. Applied egg-rr 75.8%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y}}{e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.8%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y}}{e^{b}} \]

       2. *-rgt-identity 75.8%

          \[\leadsto x \cdot \frac{\frac{\frac{\color{blue}{{a}^{t}}}{a}}{y}}{e^{b}} \]

   11. Simplified 75.8%

       \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t}}{a}}}{y}}{e^{b}} \]

   12. Taylor expanded in t around 0 57.1%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 55.5%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

       2. *-commutative 55.5%

          \[\leadsto \frac{x}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

       3. associate-*l* 57.1%

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   14. Simplified 57.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   15. Taylor expanded in b around 0 45.2%

       \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a + a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.6% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+107) (/ (- x (* x b)) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+107) {
		tmp = (x - (x * b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+107)) then
        tmp = (x - (x * b)) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+107) {
		tmp = (x - (x * b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+107:
		tmp = (x - (x * b)) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+107)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	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 (b <= -2e+107)
		tmp = (x - (x * b)) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+107], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9999999999999999e107

   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. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 93.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 93.2%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 93.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 93.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 77.5%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 77.5%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 77.5%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 78.2%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + b \cdot \left(-0.16666666666666666 \cdot \frac{b \cdot x}{y} + 0.5 \cdot \frac{x}{y}\right)\right) + \frac{x}{y}} \]

   9. Taylor expanded in y around 0 82.2%

      \[\leadsto \color{blue}{\frac{x + b \cdot \left(-1 \cdot x + b \cdot \left(-0.16666666666666666 \cdot \left(b \cdot x\right) + 0.5 \cdot x\right)\right)}{y}} \]

   10. Taylor expanded in b around 0 51.8%

       \[\leadsto \frac{x + \color{blue}{-1 \cdot \left(b \cdot x\right)}}{y} \]
   11. Step-by-step derivation

       1. associate-*r* 51.8%

          \[\leadsto \frac{x + \color{blue}{\left(-1 \cdot b\right) \cdot x}}{y} \]

       2. neg-mul-1 51.8%

          \[\leadsto \frac{x + \color{blue}{\left(-b\right)} \cdot x}{y} \]

   12. Simplified 51.8%

       \[\leadsto \frac{x + \color{blue}{\left(-b\right) \cdot x}}{y} \]

   if -1.9999999999999999e107 < b

   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. *-commutative 98.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 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. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]

   6. Taylor expanded in b around 0 57.6%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right)}} \cdot \frac{x}{y} \]
   7. Step-by-step derivation

      1. exp-to-pow 58.2%

         \[\leadsto \color{blue}{{a}^{\left(t - 1\right)}} \cdot \frac{x}{y} \]

      2. sub-neg 58.2%

         \[\leadsto {a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot \frac{x}{y} \]

      3. metadata-eval 58.2%

         \[\leadsto {a}^{\left(t + \color{blue}{-1}\right)} \cdot \frac{x}{y} \]

      4. +-commutative 58.2%

         \[\leadsto {a}^{\color{blue}{\left(-1 + t\right)}} \cdot \frac{x}{y} \]

   8. Simplified 58.2%

      \[\leadsto \color{blue}{{a}^{\left(-1 + t\right)}} \cdot \frac{x}{y} \]

   9. Taylor expanded in t around 0 37.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 98.3%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 89.4%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 89.4%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 89.4%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 89.4%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 89.4%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 89.4%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 73.4%

   \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]

6. Taylor expanded in b around 0 55.8%

   \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right)}} \cdot \frac{x}{y} \]
7. Step-by-step derivation

   1. exp-to-pow 56.2%

      \[\leadsto \color{blue}{{a}^{\left(t - 1\right)}} \cdot \frac{x}{y} \]

   2. sub-neg 56.2%

      \[\leadsto {a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot \frac{x}{y} \]

   3. metadata-eval 56.2%

      \[\leadsto {a}^{\left(t + \color{blue}{-1}\right)} \cdot \frac{x}{y} \]

   4. +-commutative 56.2%

      \[\leadsto {a}^{\color{blue}{\left(-1 + t\right)}} \cdot \frac{x}{y} \]

8. Simplified 56.2%

   \[\leadsto \color{blue}{{a}^{\left(-1 + t\right)}} \cdot \frac{x}{y} \]

9. Taylor expanded in t around 0 34.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 34.8%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Alternative 23: 16.2% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / 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 / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 98.3%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 89.4%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 89.4%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 89.4%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. sub-neg 89.4%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   6. metadata-eval 89.4%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

3. Simplified 89.4%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 46.1%

   \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
6. Step-by-step derivation

   1. neg-mul-1 46.1%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

7. Simplified 46.1%

   \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

8. Taylor expanded in b around 0 17.1%

   \[\leadsto \color{blue}{\frac{x}{y}} \]

9. Final simplification 17.1%

   \[\leadsto \frac{x}{y} \]
10. Add Preprocessing

Developer target: 72.7% 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 2024096 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))