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

Percentage Accurate: 98.6% → 98.6%

Time: 21.5s

Alternatives: 29

Speedup: 1.0×

• 47.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.6% 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: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.2%

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

3. Final simplification 98.2%

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

Alternative 2: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.05e+36)
   (* x (/ (exp (- (- (* y (log z)) (log a)) b)) y))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.05e+36) {
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.05d+36) then
        tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y)
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.05e+36) {
		tmp = x * (Math.exp((((y * Math.log(z)) - Math.log(a)) - b)) / y);
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.05e+36:
		tmp = x * (math.exp((((y * math.log(z)) - math.log(a)) - b)) / y)
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.05e+36)
		tmp = Float64(x * Float64(exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b)) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.05e+36)
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.05e+36], 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[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.05000000000000002e36

   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* 88.1%

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

      3. associate--l+ 88.1%

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

      4. fma-define 88.1%

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

      5. sub-neg 88.1%

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

      6. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around 0 90.2%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. mul-1-neg 90.1%

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

      4. unsub-neg 90.1%

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

   7. Simplified 90.1%

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

   if 1.05000000000000002e36 < t

   1. Initial program 100.0%

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

      1. *-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* 91.3%

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

      3. associate--l+ 91.3%

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

      4. fma-define 91.3%

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

      5. sub-neg 91.3%

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

      6. metadata-eval 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 94.3%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+264} \lor \neg \left(t \leq -3.6 \cdot 10^{+80}\right) \land \left(t \leq -2.1 \cdot 10^{-59} \lor \neg \left(t \leq 1.32 \cdot 10^{+38}\right)\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e+264)
         (and (not (<= t -3.6e+80))
              (or (<= t -2.1e-59) (not (<= t 1.32e+38)))))
   (/ (* x (pow a (+ t -1.0))) y)
   (* x (/ (/ (pow z y) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+264) || (!(t <= -3.6e+80) && ((t <= -2.1e-59) || !(t <= 1.32e+38)))) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = x * ((pow(z, y) / a) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.05d+264)) .or. (.not. (t <= (-3.6d+80))) .and. (t <= (-2.1d-59)) .or. (.not. (t <= 1.32d+38))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = x * (((z ** y) / a) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+264) || (!(t <= -3.6e+80) && ((t <= -2.1e-59) || !(t <= 1.32e+38)))) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = x * ((Math.pow(z, y) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e+264) or (not (t <= -3.6e+80) and ((t <= -2.1e-59) or not (t <= 1.32e+38))):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = x * ((math.pow(z, y) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e+264) || (!(t <= -3.6e+80) && ((t <= -2.1e-59) || !(t <= 1.32e+38))))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.05e+264) || (~((t <= -3.6e+80)) && ((t <= -2.1e-59) || ~((t <= 1.32e+38)))))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = x * (((z ^ y) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e+264], And[N[Not[LessEqual[t, -3.6e+80]], $MachinePrecision], Or[LessEqual[t, -2.1e-59], N[Not[LessEqual[t, 1.32e+38]], $MachinePrecision]]]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05000000000000005e264 or -3.59999999999999995e80 < t < -2.09999999999999997e-59 or 1.32e38 < t

   1. Initial program 100.0%

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

      1. *-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* 89.4%

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

      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 93.7%

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

   6. Taylor expanded in b around 0 91.6%

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

      1. exp-to-pow 91.6%

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

      2. sub-neg 91.6%

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

      3. metadata-eval 91.6%

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

      4. +-commutative 91.6%

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

   8. Simplified 91.6%

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

   if -1.05000000000000005e264 < t < -3.59999999999999995e80 or -2.09999999999999997e-59 < t < 1.32e38

   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* 96.4%

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

      2. associate--l+ 96.4%

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

      3. exp-sum 77.9%

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

      4. associate-/l* 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. exp-diff 73.0%

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

      8. *-commutative 73.0%

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

      9. exp-to-pow 74.2%

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

      10. sub-neg 74.2%

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

      11. metadata-eval 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in t around 0 78.6%

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

      1. associate-/r* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+264} \lor \neg \left(t \leq -3.6 \cdot 10^{+80}\right) \land \left(t \leq -2.1 \cdot 10^{-59} \lor \neg \left(t \leq 1.32 \cdot 10^{+38}\right)\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+218} \lor \neg \left(y \leq 8.5 \cdot 10^{+159}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+218) (not (<= y 8.5e+159)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+218) || !(y <= 8.5e+159)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d+218)) .or. (.not. (y <= 8.5d+159))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+218) || !(y <= 8.5e+159)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+218) or not (y <= 8.5e+159):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+218) || !(y <= 8.5e+159))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+218) || ~((y <= 8.5e+159)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+218], N[Not[LessEqual[y, 8.5e+159]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0499999999999999e218 or 8.50000000000000076e159 < y

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 53.1%

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

      4. associate-/l* 49.0%

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

      5. *-commutative 49.0%

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

      6. exp-to-pow 49.0%

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

      7. exp-diff 42.9%

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

      8. *-commutative 42.9%

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

      9. exp-to-pow 42.9%

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

      10. sub-neg 42.9%

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

      11. metadata-eval 42.9%

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

   3. Simplified 42.9%

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

   5. Taylor expanded in t around 0 51.1%

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

      1. associate-/r* 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in b around 0 94.0%

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

   if -1.0499999999999999e218 < y < 8.50000000000000076e159

   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. *-commutative 97.7%

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

      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 y around 0 89.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+218} \lor \neg \left(y \leq 8.5 \cdot 10^{+159}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 10200000000:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.3e+54)
   (/ x (* y (exp b)))
   (if (<= b 10200000000.0)
     (* x (* (pow a (+ t -1.0)) (/ (pow z y) y)))
     (/ x (* y (* a (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.3e+54) {
		tmp = x / (y * exp(b));
	} else if (b <= 10200000000.0) {
		tmp = x * (pow(a, (t + -1.0)) * (pow(z, y) / y));
	} else {
		tmp = x / (y * (a * 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 <= (-5.3d+54)) then
        tmp = x / (y * exp(b))
    else if (b <= 10200000000.0d0) then
        tmp = x * ((a ** (t + (-1.0d0))) * ((z ** y) / y))
    else
        tmp = x / (y * (a * 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 <= -5.3e+54) {
		tmp = x / (y * Math.exp(b));
	} else if (b <= 10200000000.0) {
		tmp = x * (Math.pow(a, (t + -1.0)) * (Math.pow(z, y) / y));
	} else {
		tmp = x / (y * (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.3e+54:
		tmp = x / (y * math.exp(b))
	elif b <= 10200000000.0:
		tmp = x * (math.pow(a, (t + -1.0)) * (math.pow(z, y) / y))
	else:
		tmp = x / (y * (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.3e+54)
		tmp = Float64(x / Float64(y * exp(b)));
	elseif (b <= 10200000000.0)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) * Float64((z ^ y) / y)));
	else
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.3e+54)
		tmp = x / (y * exp(b));
	elseif (b <= 10200000000.0)
		tmp = x * ((a ^ (t + -1.0)) * ((z ^ y) / y));
	else
		tmp = x / (y * (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.3e+54], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 10200000000.0], 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[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.30000000000000018e54

   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* 94.5%

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

      3. associate--l+ 94.5%

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

      4. fma-define 94.5%

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

      5. sub-neg 94.5%

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

      6. metadata-eval 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in b around inf 83.8%

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

      1. neg-mul-1 83.8%

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

   7. Simplified 83.8%

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

      1. exp-neg 83.8%

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

      2. frac-times 89.3%

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

      3. *-un-lft-identity 89.3%

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

      4. *-commutative 89.3%

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

   9. Applied egg-rr 89.3%

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

   if -5.30000000000000018e54 < b < 1.02e10

   1. Initial program 96.7%

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

      1. associate-/l* 95.9%

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

      2. associate--l+ 95.9%

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

      3. exp-sum 83.1%

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

      4. associate-/l* 81.7%

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

      5. *-commutative 81.7%

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

      6. exp-to-pow 81.7%

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

      7. exp-diff 80.3%

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

      8. *-commutative 80.3%

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

      9. exp-to-pow 81.7%

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

      10. sub-neg 81.7%

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

      11. metadata-eval 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in b around 0 83.2%

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

      1. associate-/l* 83.2%

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

      2. exp-to-pow 84.5%

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

      3. sub-neg 84.5%

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

      4. metadata-eval 84.5%

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

   7. Simplified 84.5%

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

   if 1.02e10 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 56.7%

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

      4. associate-/l* 56.7%

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

      5. *-commutative 56.7%

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

      6. exp-to-pow 56.7%

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

      7. exp-diff 46.7%

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

      8. *-commutative 46.7%

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

      9. exp-to-pow 46.7%

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

      10. sub-neg 46.7%

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

      11. metadata-eval 46.7%

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

   3. Simplified 46.7%

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

   5. Taylor expanded in t around 0 55.1%

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

      1. associate-/r* 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in y around 0 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*l* 77.0%

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

      3. *-commutative 77.0%

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

   10. Simplified 77.0%

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

Alternative 6: 79.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -410000 \lor \neg \left(y \leq 1.95 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -410000.0) (not (<= y 1.95e+154)))
   (* x (/ (/ (pow z y) a) y))
   (/ (/ (* x (pow a (+ t -1.0))) (exp b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -410000.0) || !(y <= 1.95e+154)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = ((x * pow(a, (t + -1.0))) / exp(b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-410000.0d0)) .or. (.not. (y <= 1.95d+154))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = ((x * (a ** (t + (-1.0d0)))) / exp(b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -410000.0) || !(y <= 1.95e+154)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = ((x * Math.pow(a, (t + -1.0))) / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -410000.0) or not (y <= 1.95e+154):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = ((x * math.pow(a, (t + -1.0))) / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -410000.0) || !(y <= 1.95e+154))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(Float64(x * (a ^ Float64(t + -1.0))) / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -410000.0) || ~((y <= 1.95e+154)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = ((x * (a ^ (t + -1.0))) / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -410000.0], N[Not[LessEqual[y, 1.95e+154]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e5 or 1.9500000000000001e154 < y

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 54.6%

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

      4. associate-/l* 52.6%

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

      5. *-commutative 52.6%

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

      6. exp-to-pow 52.6%

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

      7. exp-diff 47.4%

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

      8. *-commutative 47.4%

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

      9. exp-to-pow 47.4%

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

      10. sub-neg 47.4%

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

      11. metadata-eval 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in t around 0 53.8%

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

      1. associate-/r* 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in b around 0 79.7%

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

   if -4.1e5 < y < 1.9500000000000001e154

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-/l* 90.4%

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

      3. associate--l+ 90.4%

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

      4. fma-define 90.4%

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

      5. sub-neg 90.4%

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

      6. metadata-eval 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around 0 92.3%

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

      1. div-exp 85.4%

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

      2. associate-/l* 82.2%

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

      3. exp-to-pow 83.2%

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

      4. sub-neg 83.2%

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

      5. metadata-eval 83.2%

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

   7. Simplified 83.2%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -410000 \lor \neg \left(y \leq 1.95 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 280000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= b -2.45e+40)
     (/ x (* y (exp b)))
     (if (<= b -1.4e-97)
       t_1
       (if (<= b -2.2e-258)
         (* x (/ (/ (pow z y) a) y))
         (if (<= b 280000000.0) t_1 (/ x (* y (* a (exp b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (b <= -2.45e+40) {
		tmp = x / (y * exp(b));
	} else if (b <= -1.4e-97) {
		tmp = t_1;
	} else if (b <= -2.2e-258) {
		tmp = x * ((pow(z, y) / a) / y);
	} else if (b <= 280000000.0) {
		tmp = t_1;
	} else {
		tmp = x / (y * (a * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (b <= (-2.45d+40)) then
        tmp = x / (y * exp(b))
    else if (b <= (-1.4d-97)) then
        tmp = t_1
    else if (b <= (-2.2d-258)) then
        tmp = x * (((z ** y) / a) / y)
    else if (b <= 280000000.0d0) then
        tmp = t_1
    else
        tmp = x / (y * (a * 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 t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (b <= -2.45e+40) {
		tmp = x / (y * Math.exp(b));
	} else if (b <= -1.4e-97) {
		tmp = t_1;
	} else if (b <= -2.2e-258) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else if (b <= 280000000.0) {
		tmp = t_1;
	} else {
		tmp = x / (y * (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if b <= -2.45e+40:
		tmp = x / (y * math.exp(b))
	elif b <= -1.4e-97:
		tmp = t_1
	elif b <= -2.2e-258:
		tmp = x * ((math.pow(z, y) / a) / y)
	elif b <= 280000000.0:
		tmp = t_1
	else:
		tmp = x / (y * (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (b <= -2.45e+40)
		tmp = Float64(x / Float64(y * exp(b)));
	elseif (b <= -1.4e-97)
		tmp = t_1;
	elseif (b <= -2.2e-258)
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	elseif (b <= 280000000.0)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (b <= -2.45e+40)
		tmp = x / (y * exp(b));
	elseif (b <= -1.4e-97)
		tmp = t_1;
	elseif (b <= -2.2e-258)
		tmp = x * (((z ^ y) / a) / y);
	elseif (b <= 280000000.0)
		tmp = t_1;
	else
		tmp = x / (y * (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.45e+40], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.4e-97], t$95$1, If[LessEqual[b, -2.2e-258], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 280000000.0], t$95$1, N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.45000000000000024e40

   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* 94.6%

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

      3. associate--l+ 94.6%

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

      4. fma-define 94.6%

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

      5. sub-neg 94.6%

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

      6. metadata-eval 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in b around inf 84.1%

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

      1. neg-mul-1 84.1%

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

   7. Simplified 84.1%

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

      1. exp-neg 84.1%

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

      2. frac-times 89.5%

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

      3. *-un-lft-identity 89.5%

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

      4. *-commutative 89.5%

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

   9. Applied egg-rr 89.5%

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

   if -2.45000000000000024e40 < b < -1.4000000000000001e-97 or -2.20000000000000015e-258 < b < 2.8e8

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-/l* 92.7%

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

      3. associate--l+ 92.7%

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

      4. fma-define 92.7%

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

      5. sub-neg 92.7%

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

      6. metadata-eval 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 80.3%

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

   6. Taylor expanded in b around 0 79.8%

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

      1. exp-to-pow 80.8%

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

      2. sub-neg 80.8%

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

      3. metadata-eval 80.8%

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

      4. +-commutative 80.8%

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

   8. Simplified 80.8%

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

   if -1.4000000000000001e-97 < b < -2.20000000000000015e-258

   1. Initial program 95.5%

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

      1. associate-/l* 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 83.1%

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

      4. associate-/l* 80.2%

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

      5. *-commutative 80.2%

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

      6. exp-to-pow 80.2%

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

      7. exp-diff 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 82.3%

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

      10. sub-neg 82.3%

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

      11. metadata-eval 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in t around 0 70.8%

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

      1. associate-/r* 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in b around 0 91.3%

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

   if 2.8e8 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 56.5%

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

      4. associate-/l* 56.5%

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

      5. *-commutative 56.5%

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

      6. exp-to-pow 56.5%

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

      7. exp-diff 46.8%

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

      8. *-commutative 46.8%

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

      9. exp-to-pow 46.8%

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

      10. sub-neg 46.8%

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

      11. metadata-eval 46.8%

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

   3. Simplified 46.8%

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

   5. Taylor expanded in t around 0 54.9%

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

      1. associate-/r* 54.9%

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

   7. Simplified 54.9%

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

   8. Taylor expanded in y around 0 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*l* 76.2%

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

      3. *-commutative 76.2%

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

   10. Simplified 76.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 280000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -22500000:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y} + \frac{x}{y} \cdot 0.5\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -22500000.0)
   (+
    (/ x y)
    (*
     b
     (-
      (* b (+ (* -0.16666666666666666 (/ (* x b) y)) (* (/ x y) 0.5)))
      (/ x y))))
   (if (<= b 2.75e-14)
     (/ 1.0 (* a (/ y x)))
     (if (<= b 6.8e+31)
       (* x (/ (exp b) y))
       (/
        x
        (*
         a
         (*
          y
          (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -22500000.0) {
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)));
	} else if (b <= 2.75e-14) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 6.8e+31) {
		tmp = x * (exp(b) / y);
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 <= (-22500000.0d0)) then
        tmp = (x / y) + (b * ((b * (((-0.16666666666666666d0) * ((x * b) / y)) + ((x / y) * 0.5d0))) - (x / y)))
    else if (b <= 2.75d-14) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 6.8d+31) then
        tmp = x * (exp(b) / y)
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 <= -22500000.0) {
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)));
	} else if (b <= 2.75e-14) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 6.8e+31) {
		tmp = x * (Math.exp(b) / y);
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -22500000.0:
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)))
	elif b <= 2.75e-14:
		tmp = 1.0 / (a * (y / x))
	elif b <= 6.8e+31:
		tmp = x * (math.exp(b) / y)
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -22500000.0)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(Float64(-0.16666666666666666 * Float64(Float64(x * b) / y)) + Float64(Float64(x / y) * 0.5))) - Float64(x / y))));
	elseif (b <= 2.75e-14)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 6.8e+31)
		tmp = Float64(x * Float64(exp(b) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -22500000.0)
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)));
	elseif (b <= 2.75e-14)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 6.8e+31)
		tmp = x * (exp(b) / y);
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -22500000.0], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(-0.16666666666666666 * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.75e-14], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+31], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.25e7

   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* 95.4%

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

      3. associate--l+ 95.4%

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

      4. fma-define 95.4%

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

      5. sub-neg 95.4%

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

      6. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in b around inf 81.7%

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

      1. neg-mul-1 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in b around 0 70.4%

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

   if -2.25e7 < b < 2.74999999999999996e-14

   1. Initial program 96.3%

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

      1. associate-/l* 95.4%

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

      2. associate--l+ 95.4%

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

      3. exp-sum 83.5%

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

      4. associate-/l* 81.9%

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

      5. *-commutative 81.9%

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

      6. exp-to-pow 81.9%

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

      7. exp-diff 81.9%

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

      8. *-commutative 81.9%

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

      9. exp-to-pow 83.4%

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

      10. sub-neg 83.4%

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

      11. metadata-eval 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in t around 0 64.4%

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

      1. associate-/r* 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l* 39.7%

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

      3. *-commutative 39.7%

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

   10. Simplified 39.7%

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

   11. Taylor expanded in b around 0 39.4%

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

       1. clear-num 38.7%

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

       2. inv-pow 38.7%

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

       3. *-commutative 38.7%

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

   13. Applied egg-rr 38.7%

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

       1. unpow-1 38.7%

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

       2. associate-/l* 42.5%

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

   15. Simplified 42.5%

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

   if 2.74999999999999996e-14 < b < 6.7999999999999996e31

   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* 76.9%

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

      3. associate--l+ 76.9%

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

      4. fma-define 76.9%

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

      5. sub-neg 76.9%

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

      6. metadata-eval 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in b around inf 47.0%

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

      1. neg-mul-1 47.0%

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

   7. Simplified 47.0%

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

      1. clear-num 47.0%

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

      2. un-div-inv 47.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 24.0%

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

      5. sqr-neg 24.0%

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

      6. sqrt-unprod 24.0%

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

      7. add-sqr-sqrt 24.0%

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

   9. Applied egg-rr 24.0%

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

       1. associate-/r/ 47.0%

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

   11. Simplified 47.0%

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

   if 6.7999999999999996e31 < 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* 78.8%

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

      3. associate--l+ 78.8%

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

      4. fma-define 78.8%

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

      5. sub-neg 78.8%

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

      6. metadata-eval 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in y around 0 86.7%

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

      1. div-exp 71.3%

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

      2. associate-/l* 65.6%

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

      3. exp-to-pow 65.6%

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

      4. sub-neg 65.6%

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

      5. metadata-eval 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in t around 0 81.1%

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

   9. Taylor expanded in b around 0 60.7%

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

   10. Taylor expanded in a around 0 69.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -22500000:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y} + \frac{x}{y} \cdot 0.5\right) - \frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00085 \lor \neg \left(b \leq 1.5 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.00085) (not (<= b 1.5e-29)))
   (/ (/ x (* a (exp b))) y)
   (* x (/ (/ (pow z y) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.00085) || !(b <= 1.5e-29)) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = x * ((pow(z, y) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.00085d0)) .or. (.not. (b <= 1.5d-29))) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = x * (((z ** y) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.00085) || !(b <= 1.5e-29)) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.00085) or not (b <= 1.5e-29):
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.00085) || !(b <= 1.5e-29))
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	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 <= -0.00085) || ~((b <= 1.5e-29)))
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.00085], N[Not[LessEqual[b, 1.5e-29]], $MachinePrecision]], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $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 < -8.49999999999999953e-4 or 1.5000000000000001e-29 < b

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 86.4%

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

      3. associate--l+ 86.4%

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

      4. fma-define 86.4%

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

      5. sub-neg 86.4%

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

      6. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around 0 87.4%

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

      1. div-exp 72.4%

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

      2. associate-/l* 65.7%

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

      3. exp-to-pow 65.8%

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

      4. sub-neg 65.8%

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

      5. metadata-eval 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in t around 0 80.2%

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

   if -8.49999999999999953e-4 < b < 1.5000000000000001e-29

   1. Initial program 96.3%

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

      1. associate-/l* 96.8%

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

      2. associate--l+ 96.8%

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

      3. exp-sum 84.5%

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

      4. associate-/l* 82.9%

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

      5. *-commutative 82.9%

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

      6. exp-to-pow 82.9%

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

      7. exp-diff 82.9%

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

      8. *-commutative 82.9%

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

      9. exp-to-pow 84.4%

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

      10. sub-neg 84.4%

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

      11. metadata-eval 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around 0 65.6%

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

      1. associate-/r* 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in b around 0 72.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00085 \lor \neg \left(b \leq 1.5 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -700 \lor \neg \left(b \leq 2.75 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -700.0) (not (<= b 2.75e-14)))
   (/ x (* y (exp b)))
   (/ 1.0 (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -700.0) || !(b <= 2.75e-14)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	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 <= (-700.0d0)) .or. (.not. (b <= 2.75d-14))) then
        tmp = x / (y * exp(b))
    else
        tmp = 1.0d0 / (a * (y / x))
    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 <= -700.0) || !(b <= 2.75e-14)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -700.0) or not (b <= 2.75e-14):
		tmp = x / (y * math.exp(b))
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -700.0) || !(b <= 2.75e-14))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -700.0) || ~((b <= 2.75e-14)))
		tmp = x / (y * exp(b));
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -700.0], N[Not[LessEqual[b, 2.75e-14]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -700 or 2.74999999999999996e-14 < 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* 86.9%

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

      3. associate--l+ 86.9%

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

      4. fma-define 86.9%

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

      5. sub-neg 86.9%

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

      6. metadata-eval 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in b around inf 71.8%

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

      1. neg-mul-1 71.8%

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

   7. Simplified 71.8%

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

      1. exp-neg 71.8%

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

      2. frac-times 80.3%

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

      3. *-un-lft-identity 80.3%

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

      4. *-commutative 80.3%

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

   9. Applied egg-rr 80.3%

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

   if -700 < b < 2.74999999999999996e-14

   1. Initial program 96.3%

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

      1. associate-/l* 95.4%

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

      2. associate--l+ 95.4%

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

      3. exp-sum 83.5%

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

      4. associate-/l* 81.9%

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

      5. *-commutative 81.9%

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

      6. exp-to-pow 81.9%

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

      7. exp-diff 81.9%

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

      8. *-commutative 81.9%

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

      9. exp-to-pow 83.4%

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

      10. sub-neg 83.4%

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

      11. metadata-eval 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in t around 0 64.4%

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

      1. associate-/r* 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l* 39.7%

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

      3. *-commutative 39.7%

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

   10. Simplified 39.7%

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

   11. Taylor expanded in b around 0 39.4%

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

       1. clear-num 38.7%

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

       2. inv-pow 38.7%

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

       3. *-commutative 38.7%

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

   13. Applied egg-rr 38.7%

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

       1. unpow-1 38.7%

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

       2. associate-/l* 42.5%

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

   15. Simplified 42.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -700 \lor \neg \left(b \leq 2.75 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 78:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 78.0) (/ x (* y (* a (exp b)))) (/ x (* y (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 78.0) {
		tmp = x / (y * (a * exp(b)));
	} 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 (t <= 78.0d0) then
        tmp = x / (y * (a * exp(b)))
    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 (t <= 78.0) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 78.0:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 78.0)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	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 (t <= 78.0)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 78.0], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 78

   1. Initial program 97.4%

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

      1. associate-/l* 96.8%

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

      2. associate--l+ 96.8%

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

      3. exp-sum 76.2%

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

      4. associate-/l* 75.1%

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

      5. *-commutative 75.1%

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

      6. exp-to-pow 75.1%

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

      7. exp-diff 71.2%

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

      8. *-commutative 71.2%

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

      9. exp-to-pow 72.3%

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

      10. sub-neg 72.3%

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

      11. metadata-eval 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in t around 0 74.7%

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

      1. associate-/r* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in y around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*l* 71.1%

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

      3. *-commutative 71.1%

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

   10. Simplified 71.1%

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

   if 78 < t

   1. Initial program 100.0%

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

      1. *-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 38.7%

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

      1. neg-mul-1 38.7%

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

   7. Simplified 38.7%

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

      1. exp-neg 38.7%

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

      2. frac-times 40.0%

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

      3. *-un-lft-identity 40.0%

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

      4. *-commutative 40.0%

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

   9. Applied egg-rr 40.0%

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

Alternative 12: 58.6% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 y around 0 81.4%

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

   1. div-exp 73.6%

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

   2. associate-/l* 70.1%

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

   3. exp-to-pow 70.7%

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

   4. sub-neg 70.7%

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

   5. metadata-eval 70.7%

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

7. Simplified 70.7%

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

8. Taylor expanded in t around 0 60.9%

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

Alternative 13: 51.5% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y} + \frac{x}{y} \cdot 0.5\right) - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5)
   (+
    (/ x y)
    (*
     b
     (-
      (* b (+ (* -0.16666666666666666 (/ (* x b) y)) (* (/ x y) 0.5)))
      (/ x y))))
   (/
    (/ x (* a (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
    y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5) {
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)));
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.5d0)) then
        tmp = (x / y) + (b * ((b * (((-0.16666666666666666d0) * ((x * b) / y)) + ((x / y) * 0.5d0))) - (x / y)))
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5) {
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)));
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.5:
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)))
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.5)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * Float64(Float64(-0.16666666666666666 * Float64(Float64(x * b) / y)) + Float64(Float64(x / y) * 0.5))) - Float64(x / y))));
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.5)
		tmp = (x / y) + (b * ((b * ((-0.16666666666666666 * ((x * b) / y)) + ((x / y) * 0.5))) - (x / y)));
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(-0.16666666666666666 * N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5

   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* 95.4%

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

      3. associate--l+ 95.4%

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

      4. fma-define 95.4%

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

      5. sub-neg 95.4%

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

      6. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in b around inf 81.7%

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

      1. neg-mul-1 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in b around 0 70.4%

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

   if -1.5 < b

   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* 86.7%

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

      3. associate--l+ 86.7%

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

      4. fma-define 86.7%

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

      5. sub-neg 86.7%

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

      6. metadata-eval 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in y around 0 78.2%

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

      1. div-exp 72.4%

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

      2. associate-/l* 70.9%

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

      3. exp-to-pow 71.7%

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

      4. sub-neg 71.7%

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

      5. metadata-eval 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in t around 0 52.2%

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

   9. Taylor expanded in b around 0 44.5%

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

   10. Taylor expanded in a around 0 46.0%

       \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{x \cdot b}{y} + \frac{x}{y} \cdot 0.5\right) - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.5% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.4e+34)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b 0.5)))) y))
   (if (<= b -1.5e-257)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (/
      (/ x (* a (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.4e+34) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	} else if (b <= -1.5e-257) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.4d+34)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * 0.5d0)))) / y)
    else if (b <= (-1.5d-257)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.4e+34) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	} else if (b <= -1.5e-257) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.4e+34:
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y)
	elif b <= -1.5e-257:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.4e+34)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5)))) / y));
	elseif (b <= -1.5e-257)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.4e+34)
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	elseif (b <= -1.5e-257)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.4e+34], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e-257], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.40000000000000017e34

   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* 94.9%

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

      3. associate--l+ 94.9%

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

      4. fma-define 94.9%

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

      5. sub-neg 94.9%

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

      6. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in b around inf 79.8%

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

      1. neg-mul-1 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in b around 0 62.4%

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

   9. Taylor expanded in x around 0 64.1%

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

   10. Taylor expanded in y around 0 68.9%

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

   if -7.40000000000000017e34 < b < -1.5e-257

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-/l* 92.9%

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

      3. associate--l+ 92.9%

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

      4. fma-define 92.9%

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

      5. sub-neg 92.9%

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

      6. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around 0 74.8%

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

      1. div-exp 74.8%

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

      2. associate-/l* 73.2%

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

      3. exp-to-pow 74.6%

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

      4. sub-neg 74.6%

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

      5. metadata-eval 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in t around 0 46.5%

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

   9. Taylor expanded in b around 0 40.8%

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

       1. +-commutative 40.8%

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

       2. mul-1-neg 40.8%

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

       3. unsub-neg 40.8%

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

       4. *-commutative 40.8%

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

       5. associate-/l* 40.8%

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

   11. Simplified 40.8%

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

   12. Taylor expanded in b around inf 46.7%

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

   if -1.5e-257 < b

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-/l* 84.5%

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

      3. associate--l+ 84.5%

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

      4. fma-define 84.5%

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

      5. sub-neg 84.5%

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

      6. metadata-eval 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in y around 0 80.7%

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

      1. div-exp 72.6%

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

      2. associate-/l* 70.4%

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

      3. exp-to-pow 70.9%

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

      4. sub-neg 70.9%

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

      5. metadata-eval 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in t around 0 57.0%

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

   9. Taylor expanded in b around 0 46.2%

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

   10. Taylor expanded in a around 0 48.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.7% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (+ 1.0 (* b (+ -1.0 (* b 0.5)))) y))))
   (if (<= b -8.2e+45)
     t_1
     (if (<= b 7.5e+155)
       (/ 1.0 (* a (/ y x)))
       (if (<= b 5.4e+197) t_1 (/ x (* y (+ a (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	double tmp;
	if (b <= -8.2e+45) {
		tmp = t_1;
	} else if (b <= 7.5e+155) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 5.4e+197) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((1.0d0 + (b * ((-1.0d0) + (b * 0.5d0)))) / y)
    if (b <= (-8.2d+45)) then
        tmp = t_1
    else if (b <= 7.5d+155) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 5.4d+197) then
        tmp = t_1
    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 t_1 = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	double tmp;
	if (b <= -8.2e+45) {
		tmp = t_1;
	} else if (b <= 7.5e+155) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 5.4e+197) {
		tmp = t_1;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y)
	tmp = 0
	if b <= -8.2e+45:
		tmp = t_1
	elif b <= 7.5e+155:
		tmp = 1.0 / (a * (y / x))
	elif b <= 5.4e+197:
		tmp = t_1
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5)))) / y))
	tmp = 0.0
	if (b <= -8.2e+45)
		tmp = t_1;
	elseif (b <= 7.5e+155)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 5.4e+197)
		tmp = t_1;
	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)
	t_1 = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	tmp = 0.0;
	if (b <= -8.2e+45)
		tmp = t_1;
	elseif (b <= 7.5e+155)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 5.4e+197)
		tmp = t_1;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+45], t$95$1, If[LessEqual[b, 7.5e+155], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.4e+197], t$95$1, N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.20000000000000025e45 or 7.4999999999999999e155 < b < 5.4000000000000001e197

   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* 93.7%

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

      3. associate--l+ 93.7%

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

      4. fma-define 93.7%

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

      5. sub-neg 93.7%

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

      6. metadata-eval 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in b around inf 78.0%

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

      1. neg-mul-1 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in b around 0 55.6%

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

   9. Taylor expanded in x around 0 57.1%

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

   10. Taylor expanded in y around 0 69.3%

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

   if -8.20000000000000025e45 < b < 7.4999999999999999e155

   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* 96.6%

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

      2. associate--l+ 96.6%

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

      3. exp-sum 79.2%

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

      4. associate-/l* 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 74.5%

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

      8. *-commutative 74.5%

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

      9. exp-to-pow 75.7%

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

      10. sub-neg 75.7%

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

      11. metadata-eval 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in t around 0 63.5%

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

      1. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in y around 0 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*l* 49.5%

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

      3. *-commutative 49.5%

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

   10. Simplified 49.5%

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

   11. Taylor expanded in b around 0 35.9%

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

       1. clear-num 35.4%

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

       2. inv-pow 35.4%

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

       3. *-commutative 35.4%

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

   13. Applied egg-rr 35.4%

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

       1. unpow-1 35.4%

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

       2. associate-/l* 38.6%

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

   15. Simplified 38.6%

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

   if 5.4000000000000001e197 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 57.1%

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

      4. associate-/l* 57.1%

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

      5. *-commutative 57.1%

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

      6. exp-to-pow 57.1%

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

      7. exp-diff 52.4%

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

      8. *-commutative 52.4%

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

      9. exp-to-pow 52.4%

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

      10. sub-neg 52.4%

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

      11. metadata-eval 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in t around 0 57.3%

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

      1. associate-/r* 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in y around 0 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*l* 81.3%

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

      3. *-commutative 81.3%

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

   10. Simplified 81.3%

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

   11. Taylor expanded in b around 0 58.1%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+155}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.6% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.85)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b 0.5)))) y))
   (/
    x
    (*
     a
     (* y (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.85) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	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 <= (-1.85d0)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * 0.5d0)))) / y)
    else
        tmp = x / (a * (y * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    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 <= -1.85) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.85:
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y)
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.85)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5)))) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.85)
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.85], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8500000000000001

   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* 95.4%

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

      3. associate--l+ 95.4%

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

      4. fma-define 95.4%

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

      5. sub-neg 95.4%

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

      6. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in b around inf 81.7%

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

      1. neg-mul-1 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in b around 0 61.4%

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

   9. Taylor expanded in x around 0 61.4%

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

   10. Taylor expanded in y around 0 65.8%

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

   if -1.8500000000000001 < b

   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* 86.7%

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

      3. associate--l+ 86.7%

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

      4. fma-define 86.7%

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

      5. sub-neg 86.7%

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

      6. metadata-eval 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in y around 0 78.2%

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

      1. div-exp 72.4%

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

      2. associate-/l* 70.9%

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

      3. exp-to-pow 71.7%

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

      4. sub-neg 71.7%

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

      5. metadata-eval 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in t around 0 52.2%

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

   9. Taylor expanded in b around 0 44.5%

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

   10. Taylor expanded in a around 0 45.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 46.5% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+42)
   (* x (/ (+ 1.0 (* b (+ -1.0 (* b 0.5)))) y))
   (if (<= b 1.6e-15)
     (/ 1.0 (* a (/ y x)))
     (/ x (+ y (* b (+ y (* 0.5 (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+42) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	} else if (b <= 1.6e-15) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (b * (y + (0.5 * (y * b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.5d+42)) then
        tmp = x * ((1.0d0 + (b * ((-1.0d0) + (b * 0.5d0)))) / y)
    else if (b <= 1.6d-15) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (y + (b * (y + (0.5d0 * (y * b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+42) {
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	} else if (b <= 1.6e-15) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (b * (y + (0.5 * (y * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+42:
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y)
	elif b <= 1.6e-15:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y + (b * (y + (0.5 * (y * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+42)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5)))) / y));
	elseif (b <= 1.6e-15)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / Float64(y + Float64(b * Float64(y + Float64(0.5 * Float64(y * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.5e+42)
		tmp = x * ((1.0 + (b * (-1.0 + (b * 0.5)))) / y);
	elseif (b <= 1.6e-15)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y + (b * (y + (0.5 * (y * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+42], N[(x * N[(N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-15], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(b * N[(y + N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.50000000000000052e42

   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* 94.6%

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

      3. associate--l+ 94.6%

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

      4. fma-define 94.6%

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

      5. sub-neg 94.6%

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

      6. metadata-eval 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in b around inf 84.1%

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

      1. neg-mul-1 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in b around 0 62.2%

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

   9. Taylor expanded in x around 0 63.9%

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

   10. Taylor expanded in y around 0 69.0%

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

   if -6.50000000000000052e42 < b < 1.6e-15

   1. Initial program 96.5%

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

      1. associate-/l* 95.7%

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

      2. associate--l+ 95.7%

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

      3. exp-sum 83.0%

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

      4. associate-/l* 81.5%

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

      5. *-commutative 81.5%

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

      6. exp-to-pow 81.5%

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

      7. exp-diff 80.8%

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

      8. *-commutative 80.8%

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

      9. exp-to-pow 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 t around 0 65.0%

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

      1. associate-/r* 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in y around 0 41.8%

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

      1. *-commutative 41.8%

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

      2. associate-*l* 41.8%

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

      3. *-commutative 41.8%

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

   10. Simplified 41.8%

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

   11. Taylor expanded in b around 0 38.8%

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

       1. clear-num 38.2%

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

       2. inv-pow 38.2%

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

       3. *-commutative 38.2%

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

   13. Applied egg-rr 38.2%

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

       1. unpow-1 38.2%

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

       2. associate-/l* 43.0%

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

   15. Simplified 43.0%

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

   if 1.6e-15 < 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* 77.3%

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

      3. associate--l+ 77.3%

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

      4. fma-define 77.3%

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

      5. sub-neg 77.3%

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

      6. metadata-eval 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in b around inf 61.0%

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

      1. neg-mul-1 61.0%

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

   7. Simplified 61.0%

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

      1. exp-neg 61.0%

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

      2. frac-times 73.2%

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

      3. *-un-lft-identity 73.2%

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

      4. *-commutative 73.2%

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

   9. Applied egg-rr 73.2%

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

   10. Taylor expanded in b around 0 45.0%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(-1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+48)
   (* x (- (/ 1.0 y) (/ b y)))
   (if (<= b 2.3e+54) (/ 1.0 (* a (/ y x))) (/ x (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+48) {
		tmp = x * ((1.0 / y) - (b / y));
	} else if (b <= 2.3e+54) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (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 <= (-6.8d+48)) then
        tmp = x * ((1.0d0 / y) - (b / y))
    else if (b <= 2.3d+54) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (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 <= -6.8e+48) {
		tmp = x * ((1.0 / y) - (b / y));
	} else if (b <= 2.3e+54) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+48:
		tmp = x * ((1.0 / y) - (b / y))
	elif b <= 2.3e+54:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+48)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b / y)));
	elseif (b <= 2.3e+54)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / 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 <= -6.8e+48)
		tmp = x * ((1.0 / y) - (b / y));
	elseif (b <= 2.3e+54)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+48], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+54], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8000000000000006e48

   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* 94.6%

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

      3. associate--l+ 94.6%

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

      4. fma-define 94.6%

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

      5. sub-neg 94.6%

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

      6. metadata-eval 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in b around inf 84.1%

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

      1. neg-mul-1 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in b around 0 62.2%

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

   9. Taylor expanded in x around 0 63.9%

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

   10. Taylor expanded in b around 0 46.8%

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

       1. +-commutative 46.8%

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

       2. mul-1-neg 46.8%

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

       3. unsub-neg 46.8%

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

   12. Simplified 46.8%

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

   if -6.8000000000000006e48 < b < 2.29999999999999994e54

   1. Initial program 96.9%

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

      1. associate-/l* 96.2%

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

      2. associate--l+ 96.2%

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

      3. exp-sum 80.5%

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

      4. associate-/l* 79.2%

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

      5. *-commutative 79.2%

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

      6. exp-to-pow 79.2%

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

      7. exp-diff 76.6%

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

      8. *-commutative 76.6%

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

      9. exp-to-pow 77.9%

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

      10. sub-neg 77.9%

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

      11. metadata-eval 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in t around 0 62.8%

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

      1. associate-/r* 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in y around 0 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*l* 43.9%

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

      3. *-commutative 43.9%

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

   10. Simplified 43.9%

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

   11. Taylor expanded in b around 0 36.8%

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

       1. clear-num 36.3%

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

       2. inv-pow 36.3%

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

       3. *-commutative 36.3%

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

   13. Applied egg-rr 36.3%

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

       1. unpow-1 36.3%

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

       2. associate-/l* 39.3%

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

   15. Simplified 39.3%

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

   if 2.29999999999999994e54 < 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* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in b around inf 64.2%

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

      1. neg-mul-1 64.2%

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

   7. Simplified 64.2%

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

      1. exp-neg 64.2%

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

      2. frac-times 79.1%

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

      3. *-un-lft-identity 79.1%

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

      4. *-commutative 79.1%

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

   9. Applied egg-rr 79.1%

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

   10. Taylor expanded in b around 0 37.9%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.0% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1600:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq 1.96 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1600.0)
   (/ (* x (/ b (- a))) y)
   (if (<= b 1.96e+55) (/ 1.0 (* a (/ y x))) (/ x (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1600.0) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= 1.96e+55) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (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 <= (-1600.0d0)) then
        tmp = (x * (b / -a)) / y
    else if (b <= 1.96d+55) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (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 <= -1600.0) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= 1.96e+55) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1600.0:
		tmp = (x * (b / -a)) / y
	elif b <= 1.96e+55:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1600.0)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= 1.96e+55)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / 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 <= -1600.0)
		tmp = (x * (b / -a)) / y;
	elseif (b <= 1.96e+55)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1600.0], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.96e+55], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1600

   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* 95.4%

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

      3. associate--l+ 95.4%

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

      4. fma-define 95.4%

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

      5. sub-neg 95.4%

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

      6. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around 0 90.9%

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

      1. div-exp 77.0%

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

      2. associate-/l* 67.8%

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

      3. exp-to-pow 67.8%

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

      4. sub-neg 67.8%

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

      5. metadata-eval 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in t around 0 86.4%

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

   9. Taylor expanded in b around 0 45.1%

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

       1. +-commutative 45.1%

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

       2. mul-1-neg 45.1%

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

       3. unsub-neg 45.1%

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

       4. *-commutative 45.1%

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

       5. associate-/l* 42.1%

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

   11. Simplified 42.1%

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

   12. Taylor expanded in b around inf 45.1%

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

       1. mul-1-neg 45.1%

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

       2. *-commutative 45.1%

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

       3. associate-*r/ 42.1%

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

       4. distribute-rgt-neg-in 42.1%

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

       5. distribute-neg-frac 42.1%

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

   14. Simplified 42.1%

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

   if -1600 < b < 1.96e55

   1. Initial program 96.7%

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

      1. associate-/l* 96.0%

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

      2. associate--l+ 96.0%

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

      3. exp-sum 80.7%

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

      4. associate-/l* 79.3%

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

      5. *-commutative 79.3%

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

      6. exp-to-pow 79.3%

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

      7. exp-diff 77.2%

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

      8. *-commutative 77.2%

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

      9. exp-to-pow 78.6%

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

      10. sub-neg 78.6%

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

      11. metadata-eval 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around 0 62.6%

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

      1. associate-/r* 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around 0 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*l* 42.4%

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

      3. *-commutative 42.4%

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

   10. Simplified 42.4%

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

   11. Taylor expanded in b around 0 37.5%

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

       1. clear-num 36.9%

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

       2. inv-pow 36.9%

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

       3. *-commutative 36.9%

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

   13. Applied egg-rr 36.9%

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

       1. unpow-1 36.9%

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

       2. associate-/l* 38.8%

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

   15. Simplified 38.8%

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

   if 1.96e55 < 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* 78.7%

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

      3. associate--l+ 78.7%

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

      4. fma-define 78.7%

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

      5. sub-neg 78.7%

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

      6. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in b around inf 64.2%

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

      1. neg-mul-1 64.2%

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

   7. Simplified 64.2%

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

      1. exp-neg 64.2%

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

      2. frac-times 79.1%

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

      3. *-un-lft-identity 79.1%

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

      4. *-commutative 79.1%

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

   9. Applied egg-rr 79.1%

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

   10. Taylor expanded in b around 0 37.9%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1600:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq 1.96 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.5% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -27500:\\ \;\;\;\;\frac{x}{y} \cdot \frac{b}{-a}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -27500.0)
   (* (/ x y) (/ b (- a)))
   (if (<= b 1.1e+55) (/ 1.0 (* a (/ y x))) (/ x (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -27500.0) {
		tmp = (x / y) * (b / -a);
	} else if (b <= 1.1e+55) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (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 <= (-27500.0d0)) then
        tmp = (x / y) * (b / -a)
    else if (b <= 1.1d+55) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (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 <= -27500.0) {
		tmp = (x / y) * (b / -a);
	} else if (b <= 1.1e+55) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -27500.0:
		tmp = (x / y) * (b / -a)
	elif b <= 1.1e+55:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -27500.0)
		tmp = Float64(Float64(x / y) * Float64(b / Float64(-a)));
	elseif (b <= 1.1e+55)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / 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 <= -27500.0)
		tmp = (x / y) * (b / -a);
	elseif (b <= 1.1e+55)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -27500.0], N[(N[(x / y), $MachinePrecision] * N[(b / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+55], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -27500

   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* 95.4%

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

      3. associate--l+ 95.4%

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

      4. fma-define 95.4%

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

      5. sub-neg 95.4%

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

      6. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around 0 90.9%

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

      1. div-exp 77.0%

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

      2. associate-/l* 67.8%

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

      3. exp-to-pow 67.8%

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

      4. sub-neg 67.8%

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

      5. metadata-eval 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in t around 0 86.4%

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

   9. Taylor expanded in b around 0 45.1%

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

       1. +-commutative 45.1%

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

       2. mul-1-neg 45.1%

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

       3. unsub-neg 45.1%

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

       4. *-commutative 45.1%

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

       5. associate-/l* 42.1%

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

   11. Simplified 42.1%

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

   12. Taylor expanded in b around inf 39.2%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 39.2%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. times-frac 39.1%

          \[\leadsto -\color{blue}{\frac{b}{a} \cdot \frac{x}{y}} \]

       3. distribute-rgt-neg-in 39.1%

          \[\leadsto \color{blue}{\frac{b}{a} \cdot \left(-\frac{x}{y}\right)} \]

       4. distribute-neg-frac2 39.1%

          \[\leadsto \frac{b}{a} \cdot \color{blue}{\frac{x}{-y}} \]

   14. Simplified 39.1%

       \[\leadsto \color{blue}{\frac{b}{a} \cdot \frac{x}{-y}} \]

   if -27500 < b < 1.10000000000000005e55

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.6%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 68.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 42.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. associate-*l* 42.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

      3. *-commutative 42.4%

         \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

   10. Simplified 42.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   11. Taylor expanded in b around 0 37.5%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
   12. Step-by-step derivation

       1. clear-num 36.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. inv-pow 36.9%

          \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

       3. *-commutative 36.9%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot y}}{x}\right)}^{-1} \]

   13. Applied egg-rr 36.9%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 36.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 38.8%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 38.8%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if 1.10000000000000005e55 < 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* 78.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 64.2%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 64.2%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 64.2%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]
   8. Step-by-step derivation

      1. exp-neg 64.2%

         \[\leadsto \color{blue}{\frac{1}{e^{b}}} \cdot \frac{x}{y} \]

      2. frac-times 79.1%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{e^{b} \cdot y}} \]

      3. *-un-lft-identity 79.1%

         \[\leadsto \frac{\color{blue}{x}}{e^{b} \cdot y} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

   9. Applied egg-rr 79.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   10. Taylor expanded in b around 0 37.9%

       \[\leadsto \frac{x}{\color{blue}{y + b \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -27500:\\ \;\;\;\;\frac{x}{y} \cdot \frac{b}{-a}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\left(-b\right) \cdot \frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e+52)
   (* (- b) (/ x (* y a)))
   (if (<= b 7e+53) (/ 1.0 (* a (/ y x))) (/ x (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e+52) {
		tmp = -b * (x / (y * a));
	} else if (b <= 7e+53) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (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 <= (-1d+52)) then
        tmp = -b * (x / (y * a))
    else if (b <= 7d+53) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (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 <= -1e+52) {
		tmp = -b * (x / (y * a));
	} else if (b <= 7e+53) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e+52:
		tmp = -b * (x / (y * a))
	elif b <= 7e+53:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e+52)
		tmp = Float64(Float64(-b) * Float64(x / Float64(y * a)));
	elseif (b <= 7e+53)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / 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 <= -1e+52)
		tmp = -b * (x / (y * a));
	elseif (b <= 7e+53)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e+52], N[((-b) * N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+53], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.9999999999999999e51

   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* 94.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 94.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 94.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 94.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 94.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 92.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. div-exp 78.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. associate-/l* 71.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 71.0%

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 71.0%

         \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 71.0%

         \[\leadsto \frac{\frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 89.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 45.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 45.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 45.7%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 45.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. *-commutative 45.7%

          \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

       5. associate-/l* 42.2%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{x \cdot \frac{b}{a}}}{y} \]

   11. Simplified 42.2%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - x \cdot \frac{b}{a}}}{y} \]

   12. Taylor expanded in b around inf 38.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 38.7%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 33.6%

          \[\leadsto -\color{blue}{b \cdot \frac{x}{a \cdot y}} \]

   14. Simplified 33.6%

       \[\leadsto \color{blue}{-b \cdot \frac{x}{a \cdot y}} \]

   if -9.9999999999999999e51 < b < 7.00000000000000038e53

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 76.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 76.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.1%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 68.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 44.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 44.2%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. associate-*l* 44.2%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

      3. *-commutative 44.2%

         \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

   10. Simplified 44.2%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   11. Taylor expanded in b around 0 36.6%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
   12. Step-by-step derivation

       1. clear-num 36.0%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. inv-pow 36.0%

          \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

       3. *-commutative 36.0%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot y}}{x}\right)}^{-1} \]

   13. Applied egg-rr 36.0%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 36.0%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 39.0%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 39.0%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if 7.00000000000000038e53 < 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* 78.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 64.2%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 64.2%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 64.2%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]
   8. Step-by-step derivation

      1. exp-neg 64.2%

         \[\leadsto \color{blue}{\frac{1}{e^{b}}} \cdot \frac{x}{y} \]

      2. frac-times 79.1%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{e^{b} \cdot y}} \]

      3. *-un-lft-identity 79.1%

         \[\leadsto \frac{\color{blue}{x}}{e^{b} \cdot y} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

   9. Applied egg-rr 79.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   10. Taylor expanded in b around 0 37.9%

       \[\leadsto \frac{x}{\color{blue}{y + b \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\left(-b\right) \cdot \frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.2% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6) (- (/ x y) (/ (* x b) y)) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6) {
		tmp = (x / y) - ((x * b) / y);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.6d0)) then
        tmp = (x / y) - ((x * b) / y)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6) {
		tmp = (x / y) - ((x * b) / y);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6:
		tmp = (x / y) - ((x * b) / y)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6)
		tmp = Float64(Float64(x / y) - Float64(Float64(x * b) / y));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6)
		tmp = (x / y) - ((x * b) / y);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6], N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6000000000000001

   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* 95.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.4%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 81.7%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 81.7%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 81.7%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 48.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   if -1.6000000000000001 < b

   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* 86.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 86.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. div-exp 72.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. associate-/l* 70.9%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 71.7%

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 71.7%

         \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 71.7%

         \[\leadsto \frac{\frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 52.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 38.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6:\\ \;\;\;\;\frac{x}{y} - \frac{x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.9% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -102000:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -102000.0) (* x (- (/ 1.0 y) (/ b y))) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -102000.0) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-102000.0d0)) then
        tmp = x * ((1.0d0 / y) - (b / y))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -102000.0) {
		tmp = x * ((1.0 / y) - (b / y));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -102000.0:
		tmp = x * ((1.0 / y) - (b / y))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -102000.0)
		tmp = Float64(x * Float64(Float64(1.0 / y) - Float64(b / y)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -102000.0)
		tmp = x * ((1.0 / y) - (b / y));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -102000.0], N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -102000

   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* 95.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.4%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 81.7%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 81.7%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 81.7%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 61.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + 0.5 \cdot \frac{b \cdot x}{y}\right) + \frac{x}{y}} \]

   9. Taylor expanded in x around 0 61.4%

      \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(0.5 \cdot \frac{b}{y} - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   10. Taylor expanded in b around 0 46.7%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{y} + \frac{1}{y}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 46.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} + -1 \cdot \frac{b}{y}\right)} \]

       2. mul-1-neg 46.7%

          \[\leadsto x \cdot \left(\frac{1}{y} + \color{blue}{\left(-\frac{b}{y}\right)}\right) \]

       3. unsub-neg 46.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   12. Simplified 46.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   if -102000 < b

   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* 86.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 86.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. div-exp 72.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. associate-/l* 70.9%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 71.7%

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 71.7%

         \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 71.7%

         \[\leadsto \frac{\frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 52.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 38.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 39.0% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.52:\\ \;\;\;\;x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.52) (* 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 <= -1.52) {
		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 <= (-1.52d0)) 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 <= -1.52) {
		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 <= -1.52:
		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 <= -1.52)
		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 <= -1.52)
		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, -1.52], 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 < -1.52

   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* 95.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.4%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.4%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 95.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 95.4%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 81.7%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 81.7%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 81.7%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   8. Taylor expanded in b around 0 61.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{y} + 0.5 \cdot \frac{b \cdot x}{y}\right) + \frac{x}{y}} \]

   9. Taylor expanded in x around 0 61.4%

      \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(0.5 \cdot \frac{b}{y} - \frac{1}{y}\right) + \frac{1}{y}\right)} \]

   10. Taylor expanded in b around 0 46.7%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{y} + \frac{1}{y}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 46.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} + -1 \cdot \frac{b}{y}\right)} \]

       2. mul-1-neg 46.7%

          \[\leadsto x \cdot \left(\frac{1}{y} + \color{blue}{\left(-\frac{b}{y}\right)}\right) \]

       3. unsub-neg 46.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   12. Simplified 46.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y} - \frac{b}{y}\right)} \]

   if -1.52 < b

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 75.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 73.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 73.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 73.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 71.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 71.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 71.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 60.8%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 65.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 65.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 51.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. associate-*l* 51.4%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

      3. *-commutative 51.4%

         \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

   10. Simplified 51.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   11. Taylor expanded in b around 0 38.1%

       \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a + a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 33.9% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.26e+54) (/ 1.0 (* a (/ y x))) (/ x (+ y (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.26e+54) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (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 <= 1.26d+54) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (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 <= 1.26e+54) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.26e+54:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.26e+54)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(x / 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 <= 1.26e+54)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.26e+54], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.25999999999999995e54

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 73.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 73.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 74.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 74.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 74.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.6%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 70.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 70.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 56.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. associate-*l* 56.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

      3. *-commutative 56.1%

         \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

   10. Simplified 56.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   11. Taylor expanded in b around 0 32.0%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
   12. Step-by-step derivation

       1. clear-num 31.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} \]

       2. inv-pow 31.6%

          \[\leadsto \color{blue}{{\left(\frac{y \cdot a}{x}\right)}^{-1}} \]

       3. *-commutative 31.6%

          \[\leadsto {\left(\frac{\color{blue}{a \cdot y}}{x}\right)}^{-1} \]

   13. Applied egg-rr 31.6%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 31.6%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 32.9%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 32.9%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if 1.25999999999999995e54 < 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* 78.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 78.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 78.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 78.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 64.2%

      \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. neg-mul-1 64.2%

         \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

   7. Simplified 64.2%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]
   8. Step-by-step derivation

      1. exp-neg 64.2%

         \[\leadsto \color{blue}{\frac{1}{e^{b}}} \cdot \frac{x}{y} \]

      2. frac-times 79.1%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{e^{b} \cdot y}} \]

      3. *-un-lft-identity 79.1%

         \[\leadsto \frac{\color{blue}{x}}{e^{b} \cdot y} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

   9. Applied egg-rr 79.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   10. Taylor expanded in b around 0 37.9%

       \[\leadsto \frac{x}{\color{blue}{y + b \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.26 \cdot 10^{+54}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 32.4% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 7e+33) (/ (/ x a) y) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 7e+33) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 7d+33) then
        tmp = (x / a) / y
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 7e+33) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 7e+33:
		tmp = (x / a) / y
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 7e+33)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 7e+33)
		tmp = (x / a) / y;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 7e+33], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.0000000000000002e33

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      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 y around 0 80.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. div-exp 74.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. associate-/l* 72.5%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 73.2%

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 73.2%

         \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 73.2%

         \[\leadsto \frac{\frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 73.2%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 60.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 34.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 7.0000000000000002e33 < a

   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* 99.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 77.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 77.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 77.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 68.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 68.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 69.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 69.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 69.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 69.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.1%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 68.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 64.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 64.0%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. associate-*l* 64.0%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

      3. *-commutative 64.0%

         \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

   10. Simplified 64.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   11. Taylor expanded in b around 0 33.1%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
   12. Step-by-step derivation

       1. div-inv 33.1%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot a}} \]

       2. *-commutative 33.1%

          \[\leadsto x \cdot \frac{1}{\color{blue}{a \cdot y}} \]

   13. Applied egg-rr 33.1%

       \[\leadsto \color{blue}{x \cdot \frac{1}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 32.5% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5e-44) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5e-44) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 5d-44) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5e-44) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5e-44:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5e-44)
		tmp = Float64(Float64(x / a) / 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 (a <= 5e-44)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5e-44], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.00000000000000039e-44

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 89.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 89.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 89.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. sub-neg 89.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a - b\right)} \cdot \frac{x}{y} \]

      6. metadata-eval 89.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \left(t + \color{blue}{-1}\right) \cdot \log a - b\right)} \cdot \frac{x}{y} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \left(t + -1\right) \cdot \log a - b\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. div-exp 75.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. associate-/l* 72.2%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 72.9%

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      4. sub-neg 72.9%

         \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      5. metadata-eval 72.9%

         \[\leadsto \frac{\frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot {a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]

   8. Taylor expanded in t around 0 61.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 36.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 5.00000000000000039e-44 < a

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 77.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 76.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 76.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 76.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 68.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 68.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 69.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 69.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 69.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 60.2%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. associate-/r* 66.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   7. Simplified 66.2%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 62.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. *-commutative 62.8%

         \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

      2. associate-*l* 62.8%

         \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

      3. *-commutative 62.8%

         \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

   10. Simplified 62.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   11. Taylor expanded in b around 0 31.6%

       \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 31.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 97.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 97.7%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 76.3%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 75.5%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 75.5%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 75.5%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 69.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 69.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 70.0%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 70.0%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 70.0%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 70.0%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 64.5%

   \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
6. Step-by-step derivation

   1. associate-/r* 68.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

7. Simplified 68.0%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

8. Taylor expanded in y around 0 60.3%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
9. Step-by-step derivation

   1. *-commutative 60.3%

      \[\leadsto \frac{x}{\color{blue}{\left(y \cdot e^{b}\right) \cdot a}} \]

   2. associate-*l* 60.3%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(e^{b} \cdot a\right)}} \]

   3. *-commutative 60.3%

      \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot e^{b}\right)}} \]

10. Simplified 60.3%

    \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

11. Taylor expanded in b around 0 30.8%

    \[\leadsto \frac{x}{y \cdot \color{blue}{a}} \]
12. Add Preprocessing

Alternative 29: 16.1% 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 98.2%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
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 b around inf 45.0%

   \[\leadsto e^{\color{blue}{-1 \cdot b}} \cdot \frac{x}{y} \]
6. Step-by-step derivation

   1. neg-mul-1 45.0%

      \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

7. Simplified 45.0%

   \[\leadsto e^{\color{blue}{-b}} \cdot \frac{x}{y} \]

8. Taylor expanded in b around 0 14.1%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer target: 71.4% 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 2024086 
(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))