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

Percentage Accurate: 98.5% → 98.5%

Time: 18.2s

Alternatives: 20

Speedup: 1.0×

• 46.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 82.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+55} \lor \neg \left(y \leq 3.65\right):\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+55) (not (<= y 3.65)))
   (/ (* x (pow z y)) 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 <= -4.1e+55) || !(y <= 3.65)) {
		tmp = (x * pow(z, y)) / 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 <= (-4.1d+55)) .or. (.not. (y <= 3.65d0))) then
        tmp = (x * (z ** y)) / 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 <= -4.1e+55) || !(y <= 3.65)) {
		tmp = (x * Math.pow(z, y)) / 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 <= -4.1e+55) or not (y <= 3.65):
		tmp = (x * math.pow(z, y)) / 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 <= -4.1e+55) || !(y <= 3.65))
		tmp = Float64(Float64(x * (z ^ y)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.1e+55) || ~((y <= 3.65)))
		tmp = (x * (z ^ y)) / 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, -4.1e+55], N[Not[LessEqual[y, 3.65]], $MachinePrecision]], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.09999999999999981e55 or 3.64999999999999991 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 89.8%

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

      3. associate--l+ 89.8%

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

      4. fma-define 89.8%

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

      5. sub-neg 89.8%

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

      6. metadata-eval 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around inf 73.4%

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

      1. associate-*r/ 82.7%

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

      2. *-commutative 82.7%

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

      3. pow-to-exp 82.7%

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

   7. Applied egg-rr 82.7%

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

   if -4.09999999999999981e55 < y < 3.64999999999999991

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 96.4%

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

      1. div-exp 84.2%

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

      2. exp-to-pow 85.2%

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

      3. sub-neg 85.2%

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

      4. metadata-eval 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+55} \lor \neg \left(y \leq 3.65\right):\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+18} \lor \neg \left(t \leq 3.35\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.4e+18) (not (<= t 3.35)))
   (/ (* x (pow a t)) 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 <= -5.4e+18) || !(t <= 3.35)) {
		tmp = (x * pow(a, t)) / 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 <= (-5.4d+18)) .or. (.not. (t <= 3.35d0))) then
        tmp = (x * (a ** t)) / 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 <= -5.4e+18) || !(t <= 3.35)) {
		tmp = (x * Math.pow(a, t)) / 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 <= -5.4e+18) or not (t <= 3.35):
		tmp = (x * math.pow(a, t)) / 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 <= -5.4e+18) || !(t <= 3.35))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.4e+18) || ~((t <= 3.35)))
		tmp = (x * (a ^ t)) / 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, -5.4e+18], N[Not[LessEqual[t, 3.35]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4e18 or 3.35000000000000009 < 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* 89.5%

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

      3. associate--l+ 89.5%

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

      4. fma-define 89.5%

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

      5. sub-neg 89.5%

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

      6. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 73.0%

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

      1. *-commutative 73.0%

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

   7. Simplified 73.0%

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

      1. associate-*r/ 83.6%

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

      2. exp-to-pow 83.6%

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

   9. Applied egg-rr 83.6%

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

   if -5.4e18 < t < 3.35000000000000009

   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* 94.7%

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

      2. associate--l+ 94.7%

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

      3. exp-sum 84.1%

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

      4. associate-/l* 82.0%

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

      5. *-commutative 82.0%

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

      6. exp-to-pow 82.0%

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

      7. exp-diff 80.6%

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

      8. *-commutative 80.6%

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

      9. exp-to-pow 81.3%

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

      10. sub-neg 81.3%

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

      11. metadata-eval 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around 0 82.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+18} \lor \neg \left(t \leq 3.35\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{t}}{y}\\ t_2 := \frac{x \cdot {z}^{y}}{y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \mathbf{elif}\;y \leq 1.5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a t)) y)) (t_2 (/ (* x (pow z y)) y)))
   (if (<= y -2.3e+105)
     t_2
     (if (<= y -1.2e-41)
       t_1
       (if (<= y 1.02e-235)
         (/ x (* y (exp b)))
         (if (<= y 5.4e-136)
           (/
            (/
             x
             (*
              a
              (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
            y)
           (if (<= y 1.5) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, t)) / y;
	double t_2 = (x * pow(z, y)) / y;
	double tmp;
	if (y <= -2.3e+105) {
		tmp = t_2;
	} else if (y <= -1.2e-41) {
		tmp = t_1;
	} else if (y <= 1.02e-235) {
		tmp = x / (y * exp(b));
	} else if (y <= 5.4e-136) {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	} else if (y <= 1.5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (a ** t)) / y
    t_2 = (x * (z ** y)) / y
    if (y <= (-2.3d+105)) then
        tmp = t_2
    else if (y <= (-1.2d-41)) then
        tmp = t_1
    else if (y <= 1.02d-235) then
        tmp = x / (y * exp(b))
    else if (y <= 5.4d-136) then
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))))) / y
    else if (y <= 1.5d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, t)) / y;
	double t_2 = (x * Math.pow(z, y)) / y;
	double tmp;
	if (y <= -2.3e+105) {
		tmp = t_2;
	} else if (y <= -1.2e-41) {
		tmp = t_1;
	} else if (y <= 1.02e-235) {
		tmp = x / (y * Math.exp(b));
	} else if (y <= 5.4e-136) {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	} else if (y <= 1.5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, t)) / y
	t_2 = (x * math.pow(z, y)) / y
	tmp = 0
	if y <= -2.3e+105:
		tmp = t_2
	elif y <= -1.2e-41:
		tmp = t_1
	elif y <= 1.02e-235:
		tmp = x / (y * math.exp(b))
	elif y <= 5.4e-136:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y
	elif y <= 1.5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ t)) / y)
	t_2 = Float64(Float64(x * (z ^ y)) / y)
	tmp = 0.0
	if (y <= -2.3e+105)
		tmp = t_2;
	elseif (y <= -1.2e-41)
		tmp = t_1;
	elseif (y <= 1.02e-235)
		tmp = Float64(x / Float64(y * exp(b)));
	elseif (y <= 5.4e-136)
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))) / y);
	elseif (y <= 1.5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ t)) / y;
	t_2 = (x * (z ^ y)) / y;
	tmp = 0.0;
	if (y <= -2.3e+105)
		tmp = t_2;
	elseif (y <= -1.2e-41)
		tmp = t_1;
	elseif (y <= 1.02e-235)
		tmp = x / (y * exp(b));
	elseif (y <= 5.4e-136)
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	elseif (y <= 1.5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.3e+105], t$95$2, If[LessEqual[y, -1.2e-41], t$95$1, If[LessEqual[y, 1.02e-235], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-136], 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], If[LessEqual[y, 1.5], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2999999999999998e105 or 1.5 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 89.0%

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

      3. associate--l+ 89.0%

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

      4. fma-define 89.0%

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

      5. sub-neg 89.0%

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

      6. metadata-eval 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around inf 75.2%

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

      1. associate-*r/ 85.2%

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

      2. *-commutative 85.2%

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

      3. pow-to-exp 85.2%

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

   7. Applied egg-rr 85.2%

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

   if -2.2999999999999998e105 < y < -1.20000000000000011e-41 or 5.3999999999999997e-136 < y < 1.5

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 96.2%

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

      3. associate--l+ 96.2%

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

      4. fma-define 96.2%

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

      5. sub-neg 96.2%

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

      6. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 64.8%

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

      1. *-commutative 64.8%

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

   7. Simplified 64.8%

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

      1. associate-*r/ 66.6%

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

      2. exp-to-pow 66.6%

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

   9. Applied egg-rr 66.6%

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

   if -1.20000000000000011e-41 < y < 1.02e-235

   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* 80.5%

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

      3. associate--l+ 80.5%

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

      4. fma-define 80.5%

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

      5. sub-neg 80.5%

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

      6. metadata-eval 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in b around inf 58.7%

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

      1. neg-mul-1 58.7%

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

   7. Simplified 58.7%

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

      1. exp-neg 58.7%

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

      2. frac-times 70.7%

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

      3. *-un-lft-identity 70.7%

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

   9. Applied egg-rr 70.7%

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

   if 1.02e-235 < y < 5.3999999999999997e-136

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 98.0%

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

      1. div-exp 78.7%

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

      2. exp-to-pow 80.7%

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

      3. sub-neg 80.7%

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

      4. metadata-eval 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in t around 0 81.1%

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

   7. Taylor expanded in b around 0 84.9%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 84.9%

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

   9. Simplified 84.9%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \mathbf{elif}\;y \leq 1.5:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) y)))
   (if (<= y -2.3e+105)
     t_1
     (if (<= y -4.2e-32)
       (/ (* x (pow a t)) y)
       (if (<= y 2.9e-6) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / y;
	double tmp;
	if (y <= -2.3e+105) {
		tmp = t_1;
	} else if (y <= -4.2e-32) {
		tmp = (x * pow(a, t)) / y;
	} else if (y <= 2.9e-6) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (z ** y)) / y
    if (y <= (-2.3d+105)) then
        tmp = t_1
    else if (y <= (-4.2d-32)) then
        tmp = (x * (a ** t)) / y
    else if (y <= 2.9d-6) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(z, y)) / y;
	double tmp;
	if (y <= -2.3e+105) {
		tmp = t_1;
	} else if (y <= -4.2e-32) {
		tmp = (x * Math.pow(a, t)) / y;
	} else if (y <= 2.9e-6) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / y
	tmp = 0
	if y <= -2.3e+105:
		tmp = t_1
	elif y <= -4.2e-32:
		tmp = (x * math.pow(a, t)) / y
	elif y <= 2.9e-6:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / y)
	tmp = 0.0
	if (y <= -2.3e+105)
		tmp = t_1;
	elseif (y <= -4.2e-32)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	elseif (y <= 2.9e-6)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / y;
	tmp = 0.0;
	if (y <= -2.3e+105)
		tmp = t_1;
	elseif (y <= -4.2e-32)
		tmp = (x * (a ^ t)) / y;
	elseif (y <= 2.9e-6)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.3e+105], t$95$1, If[LessEqual[y, -4.2e-32], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.9e-6], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999998e105 or 2.9000000000000002e-6 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 89.2%

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

      3. associate--l+ 89.2%

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

      4. fma-define 89.2%

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

      5. sub-neg 89.2%

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

      6. metadata-eval 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in y around inf 73.8%

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

      1. associate-*r/ 83.6%

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

      2. *-commutative 83.6%

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

      3. pow-to-exp 83.6%

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

   7. Applied egg-rr 83.6%

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

   if -2.2999999999999998e105 < y < -4.1999999999999998e-32

   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* 100.0%

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

      3. associate--l+ 100.0%

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

      4. fma-define 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 72.4%

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

      1. *-commutative 72.4%

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

   7. Simplified 72.4%

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

      1. associate-*r/ 72.4%

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

      2. exp-to-pow 72.4%

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

   9. Applied egg-rr 72.4%

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

   if -4.1999999999999998e-32 < y < 2.9000000000000002e-6

   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. Add Preprocessing

   3. Taylor expanded in y around 0 97.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. 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. exp-to-pow 86.6%

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

      3. sub-neg 86.6%

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

      4. metadata-eval 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in t around 0 81.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.25:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 850 \lor \neg \left(b \leq 3.6 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.25)
   (* x (/ (+ 1.0 (* b (+ 1.0 (* b 0.5)))) y))
   (if (or (<= b 850.0) (not (<= b 3.6e+75)))
     (/
      (/ x (* a (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
      y)
     (* x (/ (exp b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.25) {
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y);
	} else if ((b <= 850.0) || !(b <= 3.6e+75)) {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	} else {
		tmp = x * (exp(b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.25d0)) then
        tmp = x * ((1.0d0 + (b * (1.0d0 + (b * 0.5d0)))) / y)
    else if ((b <= 850.0d0) .or. (.not. (b <= 3.6d+75))) then
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0)))))))) / y
    else
        tmp = x * (exp(b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.25) {
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y);
	} else if ((b <= 850.0) || !(b <= 3.6e+75)) {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	} else {
		tmp = x * (Math.exp(b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.25:
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y)
	elif (b <= 850.0) or not (b <= 3.6e+75):
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y
	else:
		tmp = x * (math.exp(b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.25)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))) / y));
	elseif ((b <= 850.0) || !(b <= 3.6e+75))
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))) / y);
	else
		tmp = Float64(x * Float64(exp(b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.25)
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y);
	elseif ((b <= 850.0) || ~((b <= 3.6e+75)))
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	else
		tmp = x * (exp(b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.25], N[(x * N[(N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 850.0], N[Not[LessEqual[b, 3.6e+75]], $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], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.25

   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 77.0%

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

      1. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. un-div-inv 77.0%

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

      3. add-sqr-sqrt 77.0%

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

      4. sqrt-unprod 77.0%

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

      5. sqr-neg 77.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 17.6%

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

   9. Applied egg-rr 17.6%

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

       1. associate-/r/ 20.5%

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

   11. Simplified 20.5%

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

   12. Taylor expanded in b around 0 62.8%

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

   if -0.25 < b < 850 or 3.6e75 < b

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 79.5%

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

      1. div-exp 73.5%

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

      2. exp-to-pow 74.4%

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

      3. sub-neg 74.4%

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

      4. metadata-eval 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in t around 0 58.0%

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

   7. Taylor expanded in b around 0 57.4%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 57.4%

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

   9. Simplified 57.4%

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

   if 850 < b < 3.6e75

   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* 66.7%

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

      3. associate--l+ 66.7%

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

      4. fma-define 66.7%

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

      5. sub-neg 66.7%

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

      6. metadata-eval 66.7%

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

   3. Simplified 66.7%

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

   5. Taylor expanded in b around inf 27.6%

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

      1. neg-mul-1 27.6%

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

   7. Simplified 27.6%

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

      1. clear-num 27.6%

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

      2. un-div-inv 27.6%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 40.6%

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

      5. sqr-neg 40.6%

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

      6. sqrt-unprod 40.6%

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

      7. add-sqr-sqrt 40.6%

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

   9. Applied egg-rr 40.6%

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

       1. associate-/r/ 60.6%

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

   11. Simplified 60.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.25:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{elif}\;b \leq 850 \lor \neg \left(b \leq 3.6 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+17} \lor \neg \left(t \leq 3.65\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.6e+17) (not (<= t 3.65)))
   (/ (* x (pow a t)) y)
   (/ x (* (exp b) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e+17) || !(t <= 3.65)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = x / (exp(b) * (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-8.6d+17)) .or. (.not. (t <= 3.65d0))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = x / (exp(b) * (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e+17) || !(t <= 3.65)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = x / (Math.exp(b) * (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.6e+17) or not (t <= 3.65):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = x / (math.exp(b) * (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.6e+17) || !(t <= 3.65))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x / Float64(exp(b) * Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8.6e+17) || ~((t <= 3.65)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = x / (exp(b) * (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.6e+17], N[Not[LessEqual[t, 3.65]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6e17 or 3.64999999999999991 < 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* 89.5%

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

      3. associate--l+ 89.5%

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

      4. fma-define 89.5%

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

      5. sub-neg 89.5%

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

      6. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 73.0%

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

      1. *-commutative 73.0%

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

   7. Simplified 73.0%

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

      1. associate-*r/ 83.6%

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

      2. exp-to-pow 83.6%

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

   9. Applied egg-rr 83.6%

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

   if -8.6e17 < t < 3.64999999999999991

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 75.1%

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

      1. div-exp 73.7%

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

      2. exp-to-pow 74.7%

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

      3. sub-neg 74.7%

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

      4. metadata-eval 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around 0 72.7%

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

      1. associate-*r* 65.6%

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

      2. *-commutative 65.6%

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

   8. Simplified 65.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+17} \lor \neg \left(t \leq 3.65\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{+15} \lor \neg \left(t \leq 5\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.35e+15) (not (<= t 5.0)))
   (/ (* x (pow a t)) y)
   (/ x (* y (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.35e+15) || !(t <= 5.0)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = x / (y * exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.35d+15)) .or. (.not. (t <= 5.0d0))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = x / (y * exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.35e+15) || !(t <= 5.0)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.35e+15) or not (t <= 5.0):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.35e+15) || !(t <= 5.0))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.35e+15) || ~((t <= 5.0)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.35e+15], N[Not[LessEqual[t, 5.0]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.35e15 or 5 < 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* 89.6%

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

      3. associate--l+ 89.6%

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

      4. fma-define 89.6%

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

      5. sub-neg 89.6%

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

      6. metadata-eval 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 73.3%

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

      1. *-commutative 73.3%

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

   7. Simplified 73.3%

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

      1. associate-*r/ 83.7%

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

      2. exp-to-pow 83.7%

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

   9. Applied egg-rr 83.7%

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

   if -3.35e15 < t < 5

   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. *-commutative 97.6%

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

      2. associate-/l* 85.6%

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

      3. associate--l+ 85.6%

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

      4. fma-define 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 48.6%

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

      1. neg-mul-1 48.6%

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

   7. Simplified 48.6%

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

      1. exp-neg 48.6%

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

      2. frac-times 55.7%

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

      3. *-un-lft-identity 55.7%

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

   9. Applied egg-rr 55.7%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{+15} \lor \neg \left(t \leq 5\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.092 \lor \neg \left(b \leq 2150000000000\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.092) (not (<= b 2150000000000.0)))
   (/ x (* y (exp b)))
   (/ (/ x (* a (+ 1.0 (* b (+ 1.0 (* b 0.5)))))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.092) || !(b <= 2150000000000.0)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.092d0)) .or. (.not. (b <= 2150000000000.0d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * 0.5d0)))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.092) || !(b <= 2150000000000.0)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.092) or not (b <= 2150000000000.0):
		tmp = x / (y * math.exp(b))
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.092) || !(b <= 2150000000000.0))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.092) || ~((b <= 2150000000000.0)))
		tmp = x / (y * exp(b));
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * 0.5)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.092], N[Not[LessEqual[b, 2150000000000.0]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.091999999999999998 or 2.15e12 < 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* 84.8%

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

      3. associate--l+ 84.8%

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

      4. fma-define 84.8%

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

      5. sub-neg 84.8%

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

      6. metadata-eval 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in b around inf 67.8%

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

      1. neg-mul-1 67.8%

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

   7. Simplified 67.8%

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

      1. exp-neg 67.8%

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

      2. frac-times 78.4%

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

      3. *-un-lft-identity 78.4%

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

   9. Applied egg-rr 78.4%

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

   if -0.091999999999999998 < b < 2.15e12

   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. Add Preprocessing

   3. Taylor expanded in y around 0 73.8%

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

      1. div-exp 73.0%

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

      2. exp-to-pow 74.2%

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

      3. sub-neg 74.2%

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

      4. metadata-eval 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around 0 47.0%

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

   7. Taylor expanded in b around 0 47.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.092 \lor \neg \left(b \leq 2150000000000\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.3% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.225:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.225)
   (* x (/ (+ 1.0 (* b (+ 1.0 (* b 0.5)))) 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 <= -0.225) {
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / 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 <= (-0.225d0)) then
        tmp = x * ((1.0d0 + (b * (1.0d0 + (b * 0.5d0)))) / 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 <= -0.225) {
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / 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 <= -0.225:
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / 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 <= -0.225)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))) / 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 <= -0.225)
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / 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, -0.225], N[(x * N[(N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $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 < -0.225000000000000006

   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 77.0%

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

      1. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. un-div-inv 77.0%

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

      3. add-sqr-sqrt 77.0%

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

      4. sqrt-unprod 77.0%

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

      5. sqr-neg 77.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 17.6%

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

   9. Applied egg-rr 17.6%

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

       1. associate-/r/ 20.5%

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

   11. Simplified 20.5%

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

   12. Taylor expanded in b around 0 62.8%

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

   if -0.225000000000000006 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 56.6%

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

   7. Taylor expanded in b around 0 52.8%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 52.8%

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

   9. Simplified 52.8%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.225:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + b \cdot \left(1 + b \cdot 0.5\right)\\ \mathbf{if}\;b \leq -0.24:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot t\_1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (* b (+ 1.0 (* b 0.5))))))
   (if (<= b -0.24) (* x (/ t_1 y)) (/ (/ x (* a t_1)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (b * (1.0 + (b * 0.5)));
	double tmp;
	if (b <= -0.24) {
		tmp = x * (t_1 / y);
	} else {
		tmp = (x / (a * t_1)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (b * (1.0d0 + (b * 0.5d0)))
    if (b <= (-0.24d0)) then
        tmp = x * (t_1 / y)
    else
        tmp = (x / (a * t_1)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (b * (1.0 + (b * 0.5)));
	double tmp;
	if (b <= -0.24) {
		tmp = x * (t_1 / y);
	} else {
		tmp = (x / (a * t_1)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (b * (1.0 + (b * 0.5)))
	tmp = 0
	if b <= -0.24:
		tmp = x * (t_1 / y)
	else:
		tmp = (x / (a * t_1)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5))))
	tmp = 0.0
	if (b <= -0.24)
		tmp = Float64(x * Float64(t_1 / y));
	else
		tmp = Float64(Float64(x / Float64(a * t_1)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (b * (1.0 + (b * 0.5)));
	tmp = 0.0;
	if (b <= -0.24)
		tmp = x * (t_1 / y);
	else
		tmp = (x / (a * t_1)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.24], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -0.23999999999999999

   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 77.0%

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

      1. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. un-div-inv 77.0%

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

      3. add-sqr-sqrt 77.0%

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

      4. sqrt-unprod 77.0%

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

      5. sqr-neg 77.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 17.6%

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

   9. Applied egg-rr 17.6%

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

       1. associate-/r/ 20.5%

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

   11. Simplified 20.5%

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

   12. Taylor expanded in b around 0 62.8%

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

   if -0.23999999999999999 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 56.6%

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

   7. Taylor expanded in b around 0 51.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.24:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.4% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+206}:\\ \;\;\;\;\frac{x}{y} \cdot \left(1 - b\right)\\ \mathbf{elif}\;b \leq -0.19:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+206)
   (* (/ x y) (- 1.0 b))
   (if (<= b -0.19) (/ x (* y a)) (/ (/ x (+ a (* a b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+206) {
		tmp = (x / y) * (1.0 - b);
	} else if (b <= -0.19) {
		tmp = x / (y * a);
	} 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 <= (-1.15d+206)) then
        tmp = (x / y) * (1.0d0 - b)
    else if (b <= (-0.19d0)) then
        tmp = x / (y * a)
    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 <= -1.15e+206) {
		tmp = (x / y) * (1.0 - b);
	} else if (b <= -0.19) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+206:
		tmp = (x / y) * (1.0 - b)
	elif b <= -0.19:
		tmp = x / (y * a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+206)
		tmp = Float64(Float64(x / y) * Float64(1.0 - b));
	elseif (b <= -0.19)
		tmp = Float64(x / Float64(y * a));
	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 <= -1.15e+206)
		tmp = (x / y) * (1.0 - b);
	elseif (b <= -0.19)
		tmp = x / (y * a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+206], N[(N[(x / y), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -0.19], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15000000000000008e206

   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* 96.0%

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

      3. associate--l+ 96.0%

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

      4. fma-define 96.0%

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

      5. sub-neg 96.0%

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

      6. metadata-eval 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in b around inf 80.2%

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

      1. neg-mul-1 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in b around 0 45.8%

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

      1. neg-mul-1 45.8%

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

      2. unsub-neg 45.8%

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

   10. Simplified 45.8%

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

   if -1.15000000000000008e206 < b < -0.19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.9%

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

      1. div-exp 71.0%

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

      2. exp-to-pow 71.0%

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

      3. sub-neg 71.0%

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

      4. metadata-eval 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around 0 77.5%

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

   7. Taylor expanded in b around 0 33.4%

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

   if -0.19 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 56.6%

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

   7. Taylor expanded in b around 0 41.7%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+206}:\\ \;\;\;\;\frac{x}{y} \cdot \left(1 - b\right)\\ \mathbf{elif}\;b \leq -0.19:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.7% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.25:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.25)
   (* x (/ (+ 1.0 (* b (+ 1.0 (* b 0.5)))) 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 <= -0.25) {
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / 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 <= (-0.25d0)) then
        tmp = x * ((1.0d0 + (b * (1.0d0 + (b * 0.5d0)))) / 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 <= -0.25) {
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.25:
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.25)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5)))) / 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 <= -0.25)
		tmp = x * ((1.0 + (b * (1.0 + (b * 0.5)))) / y);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.25], N[(x * N[(N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 < -0.25

   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 77.0%

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

      1. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. un-div-inv 77.0%

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

      3. add-sqr-sqrt 77.0%

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

      4. sqrt-unprod 77.0%

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

      5. sqr-neg 77.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 17.6%

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

   9. Applied egg-rr 17.6%

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

       1. associate-/r/ 20.5%

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

   11. Simplified 20.5%

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

   12. Taylor expanded in b around 0 62.8%

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

   if -0.25 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 56.6%

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

   7. Taylor expanded in b around 0 41.7%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.25:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(1 + b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.7% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.155:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.155)
   (* x (/ (+ 1.0 (* b (* b 0.5))) 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 <= -0.155) {
		tmp = x * ((1.0 + (b * (b * 0.5))) / 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 <= (-0.155d0)) then
        tmp = x * ((1.0d0 + (b * (b * 0.5d0))) / 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 <= -0.155) {
		tmp = x * ((1.0 + (b * (b * 0.5))) / y);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.155:
		tmp = x * ((1.0 + (b * (b * 0.5))) / y)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.155)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(b * 0.5))) / 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 <= -0.155)
		tmp = x * ((1.0 + (b * (b * 0.5))) / y);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.155], N[(x * N[(N[(1.0 + N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $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 < -0.154999999999999999

   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 77.0%

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

      1. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. un-div-inv 77.0%

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

      3. add-sqr-sqrt 77.0%

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

      4. sqrt-unprod 77.0%

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

      5. sqr-neg 77.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 17.6%

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

   9. Applied egg-rr 17.6%

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

       1. associate-/r/ 20.5%

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

   11. Simplified 20.5%

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

   12. Taylor expanded in b around 0 62.8%

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

   13. Taylor expanded in b around inf 62.8%

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

   if -0.154999999999999999 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 56.6%

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

   7. Taylor expanded in b around 0 41.7%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.155:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(b \cdot 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.4% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.25:\\ \;\;\;\;\left(1 + b \cdot \left(b \cdot 0.5\right)\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.25)
   (* (+ 1.0 (* b (* b 0.5))) (/ x 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 <= -0.25) {
		tmp = (1.0 + (b * (b * 0.5))) * (x / 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 <= (-0.25d0)) then
        tmp = (1.0d0 + (b * (b * 0.5d0))) * (x / 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 <= -0.25) {
		tmp = (1.0 + (b * (b * 0.5))) * (x / y);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.25:
		tmp = (1.0 + (b * (b * 0.5))) * (x / y)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.25)
		tmp = Float64(Float64(1.0 + Float64(b * Float64(b * 0.5))) * Float64(x / 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 <= -0.25)
		tmp = (1.0 + (b * (b * 0.5))) * (x / y);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.25], N[(N[(1.0 + N[(b * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / 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 < -0.25

   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 77.0%

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

      1. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in b around 0 56.2%

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

   9. Taylor expanded in b around inf 56.2%

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

       1. *-commutative 56.2%

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

   11. Simplified 56.2%

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

   if -0.25 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 56.6%

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

   7. Taylor expanded in b around 0 41.7%

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

Alternative 16: 18.8% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1e+17) (* b (/ x y)) (if (<= y 2.3e-66) (/ x y) (* x (/ b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1e+17) {
		tmp = b * (x / y);
	} else if (y <= 2.3e-66) {
		tmp = x / y;
	} else {
		tmp = x * (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 <= (-1d+17)) then
        tmp = b * (x / y)
    else if (y <= 2.3d-66) then
        tmp = x / y
    else
        tmp = x * (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 <= -1e+17) {
		tmp = b * (x / y);
	} else if (y <= 2.3e-66) {
		tmp = x / y;
	} else {
		tmp = x * (b / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1e+17:
		tmp = b * (x / y)
	elif y <= 2.3e-66:
		tmp = x / y
	else:
		tmp = x * (b / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1e+17)
		tmp = Float64(b * Float64(x / y));
	elseif (y <= 2.3e-66)
		tmp = Float64(x / y);
	else
		tmp = Float64(x * Float64(b / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1e+17)
		tmp = b * (x / y);
	elseif (y <= 2.3e-66)
		tmp = x / y;
	else
		tmp = x * (b / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1e+17], N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-66], N[(x / y), $MachinePrecision], N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e17

   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* 89.7%

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

      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 b around inf 33.0%

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

      1. neg-mul-1 33.0%

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

   7. Simplified 33.0%

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

      1. clear-num 33.0%

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

      2. un-div-inv 33.0%

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

      3. add-sqr-sqrt 17.9%

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

      4. sqrt-unprod 32.8%

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

      5. sqr-neg 32.8%

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

      6. sqrt-unprod 14.9%

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

      7. add-sqr-sqrt 24.4%

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

   9. Applied egg-rr 24.4%

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

       1. associate-/r/ 29.7%

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

   11. Simplified 29.7%

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

   12. Taylor expanded in b around 0 8.0%

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

       1. +-commutative 8.0%

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

   14. Simplified 8.0%

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

   15. Taylor expanded in b around inf 15.9%

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

       1. associate-/l* 22.4%

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

   17. Simplified 22.4%

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

   if -1e17 < y < 2.29999999999999992e-66

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-/l* 83.8%

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

      3. associate--l+ 83.8%

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

      4. fma-define 83.8%

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

      5. sub-neg 83.8%

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

      6. metadata-eval 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in b around inf 51.1%

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

      1. neg-mul-1 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in b around 0 19.9%

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

   if 2.29999999999999992e-66 < y

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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* 91.8%

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

      3. associate--l+ 91.8%

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

      4. fma-define 91.8%

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

      5. sub-neg 91.8%

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

      6. metadata-eval 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in b around inf 37.9%

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

      1. neg-mul-1 37.9%

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

   7. Simplified 37.9%

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

      1. clear-num 37.9%

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

      2. un-div-inv 37.9%

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

      3. add-sqr-sqrt 21.5%

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

      4. sqrt-unprod 29.7%

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

      5. sqr-neg 29.7%

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

      6. sqrt-unprod 8.2%

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

      7. add-sqr-sqrt 16.3%

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

   9. Applied egg-rr 16.3%

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

       1. associate-/r/ 20.4%

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

   11. Simplified 20.4%

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

   12. Taylor expanded in b around 0 9.7%

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

       1. +-commutative 9.7%

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

   14. Simplified 9.7%

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

   15. Taylor expanded in b around inf 30.2%

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

4. Final simplification 23.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.6% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.9e+190) (/ (/ x a) y) (* x (/ b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.9e+190) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (b / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 2.9d+190) then
        tmp = (x / a) / y
    else
        tmp = x * (b / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.9e+190) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (b / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.9e+190:
		tmp = (x / a) / y
	else:
		tmp = x * (b / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.9e+190)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * Float64(b / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.9e+190)
		tmp = (x / a) / y;
	else
		tmp = x * (b / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.9e+190], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.89999999999999989e190

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. div-exp 72.0%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 65.7%

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

   7. Taylor expanded in b around 0 35.3%

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

   if 2.89999999999999989e190 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 85.7%

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

      3. associate--l+ 85.7%

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

      4. fma-define 85.7%

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

      5. sub-neg 85.7%

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

      6. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around inf 34.8%

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

      1. neg-mul-1 34.8%

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

   7. Simplified 34.8%

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

      1. clear-num 34.8%

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

      2. un-div-inv 34.8%

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

      3. add-sqr-sqrt 26.2%

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

      4. sqrt-unprod 34.6%

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

      5. sqr-neg 34.6%

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

      6. sqrt-unprod 8.4%

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

      7. add-sqr-sqrt 20.6%

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

   9. Applied egg-rr 20.6%

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

       1. associate-/r/ 27.8%

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

   11. Simplified 27.8%

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

   12. Taylor expanded in b around 0 20.7%

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

       1. +-commutative 20.7%

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

   14. Simplified 20.7%

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

   15. Taylor expanded in b around inf 57.8%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.5% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 8.4e+186) (/ x (* y a)) (* x (/ b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 8.4e+186) {
		tmp = x / (y * a);
	} else {
		tmp = x * (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 <= 8.4d+186) then
        tmp = x / (y * a)
    else
        tmp = x * (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 <= 8.4e+186) {
		tmp = x / (y * a);
	} else {
		tmp = x * (b / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 8.4e+186:
		tmp = x / (y * a)
	else:
		tmp = x * (b / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 8.4e+186)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x * Float64(b / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 8.4e+186)
		tmp = x / (y * a);
	else
		tmp = x * (b / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 8.4e+186], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.4000000000000001e186

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. div-exp 72.0%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 65.7%

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

   7. Taylor expanded in b around 0 31.6%

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

   if 8.4000000000000001e186 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 85.7%

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

      3. associate--l+ 85.7%

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

      4. fma-define 85.7%

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

      5. sub-neg 85.7%

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

      6. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around inf 34.8%

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

      1. neg-mul-1 34.8%

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

   7. Simplified 34.8%

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

      1. clear-num 34.8%

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

      2. un-div-inv 34.8%

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

      3. add-sqr-sqrt 26.2%

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

      4. sqrt-unprod 34.6%

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

      5. sqr-neg 34.6%

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

      6. sqrt-unprod 8.4%

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

      7. add-sqr-sqrt 20.6%

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

   9. Applied egg-rr 20.6%

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

       1. associate-/r/ 27.8%

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

   11. Simplified 27.8%

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

   12. Taylor expanded in b around 0 20.7%

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

       1. +-commutative 20.7%

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

   14. Simplified 20.7%

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

   15. Taylor expanded in b around inf 57.8%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.4 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 18.5% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e-184) (/ x y) (* b (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e-184) {
		tmp = x / y;
	} else {
		tmp = b * (x / 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 <= (-1.8d-184)) then
        tmp = x / y
    else
        tmp = b * (x / 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 <= -1.8e-184) {
		tmp = x / y;
	} else {
		tmp = b * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e-184:
		tmp = x / y
	else:
		tmp = b * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e-184)
		tmp = Float64(x / y);
	else
		tmp = Float64(b * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e-184)
		tmp = x / y;
	else
		tmp = b * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e-184], N[(x / y), $MachinePrecision], N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8000000000000001e-184

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 90.6%

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

      3. associate--l+ 90.6%

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

      4. fma-define 90.6%

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

      5. sub-neg 90.6%

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

      6. metadata-eval 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in b around inf 62.7%

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

      1. neg-mul-1 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in b around 0 19.3%

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

   if -1.8000000000000001e-184 < b

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-/l* 85.4%

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

      3. associate--l+ 85.4%

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

      4. fma-define 85.4%

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

      5. sub-neg 85.4%

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

      6. metadata-eval 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in b around inf 31.0%

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

      1. neg-mul-1 31.0%

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

   7. Simplified 31.0%

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

      1. clear-num 31.0%

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

      2. un-div-inv 31.0%

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

      3. add-sqr-sqrt 2.4%

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

      4. sqrt-unprod 17.8%

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

      5. sqr-neg 17.8%

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

      6. sqrt-unprod 15.4%

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

      7. add-sqr-sqrt 17.8%

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

   9. Applied egg-rr 17.8%

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

       1. associate-/r/ 21.7%

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

   11. Simplified 21.7%

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

   12. Taylor expanded in b around 0 12.0%

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

       1. +-commutative 12.0%

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

   14. Simplified 12.0%

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

   15. Taylor expanded in b around inf 18.5%

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

       1. associate-/l* 23.2%

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

   17. Simplified 23.2%

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

Alternative 20: 16.6% 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 98.7%

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

   1. *-commutative 98.7%

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

   2. associate-/l* 87.4%

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

   3. associate--l+ 87.4%

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

   4. fma-define 87.4%

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

   5. sub-neg 87.4%

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

   6. metadata-eval 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in b around inf 43.2%

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

   1. neg-mul-1 43.2%

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

7. Simplified 43.2%

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

8. Taylor expanded in b around 0 16.0%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer Target 1: 72.2% 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 2024157 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))