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

Percentage Accurate: 98.6% → 98.6%

Time: 19.2s

Alternatives: 19

Speedup: 1.0×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

3. Final simplification 98.1%

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

Alternative 2: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+118}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+18)
   (/ (* x (/ (pow z y) y)) a)
   (if (<= y 3.9e+118)
     (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)
     (/ (* x (exp (* y (log z)))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+18) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else if (y <= 3.9e+118) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * exp((y * log(z)))) / 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 <= (-2.3d+18)) then
        tmp = (x * ((z ** y) / y)) / a
    else if (y <= 3.9d+118) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = (x * exp((y * log(z)))) / 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 <= -2.3e+18) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else if (y <= 3.9e+118) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * Math.exp((y * Math.log(z)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.3e+18:
		tmp = (x * (math.pow(z, y) / y)) / a
	elif y <= 3.9e+118:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = (x * math.exp((y * math.log(z)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+18)
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	elseif (y <= 3.9e+118)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(y * log(z)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.3e+18)
		tmp = (x * ((z ^ y) / y)) / a;
	elseif (y <= 3.9e+118)
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = (x * exp((y * log(z)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+18], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.9e+118], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e18

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 66.7%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 88.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 88.5%

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

   if -2.3e18 < y < 3.9e118

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 91.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 91.2%

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

   if 3.9e118 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 89.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 89.9%

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

Alternative 3: 78.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-24}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z}}{y}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+112}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.65e-24)
   (/ (* x (exp (* y (log z)))) y)
   (if (<= y 8.4e+112)
     (/ (* x (pow a t)) (* y (* a (exp b))))
     (/ (* x (/ (pow z y) y)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e-24) {
		tmp = (x * exp((y * log(z)))) / y;
	} else if (y <= 8.4e+112) {
		tmp = (x * pow(a, t)) / (y * (a * exp(b)));
	} else {
		tmp = (x * (pow(z, y) / y)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.65d-24)) then
        tmp = (x * exp((y * log(z)))) / y
    else if (y <= 8.4d+112) then
        tmp = (x * (a ** t)) / (y * (a * exp(b)))
    else
        tmp = (x * ((z ** y) / y)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e-24) {
		tmp = (x * Math.exp((y * Math.log(z)))) / y;
	} else if (y <= 8.4e+112) {
		tmp = (x * Math.pow(a, t)) / (y * (a * Math.exp(b)));
	} else {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.65e-24:
		tmp = (x * math.exp((y * math.log(z)))) / y
	elif y <= 8.4e+112:
		tmp = (x * math.pow(a, t)) / (y * (a * math.exp(b)))
	else:
		tmp = (x * (math.pow(z, y) / y)) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.65e-24)
		tmp = Float64(Float64(x * exp(Float64(y * log(z)))) / y);
	elseif (y <= 8.4e+112)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.65e-24)
		tmp = (x * exp((y * log(z)))) / y;
	elseif (y <= 8.4e+112)
		tmp = (x * (a ^ t)) / (y * (a * exp(b)));
	else
		tmp = (x * ((z ^ y) / y)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.65e-24], N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.4e+112], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.64999999999999992e-24

   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 inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(y \cdot \log z\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \log z\right)\right)\right), y\right) \]

      2. log-lowering-log.f64 83.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{log.f64}\left(z\right)\right)\right)\right), y\right) \]

   5. Simplified 83.9%

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

   if -1.64999999999999992e-24 < y < 8.3999999999999996e112

   1. Initial program 96.7%

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. associate-/l/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}\right), \color{blue}{\left(y \cdot e^{b}\right)}\right) \]

   3. Simplified 76.2%

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

   5. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(e^{b} \cdot e^{\log a \cdot \left(1 - t\right)}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{e^{b}} \cdot e^{\log a \cdot \left(1 - t\right)}\right)\right) \]

      4. exp-prod N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot {\left(e^{\log a}\right)}^{\color{blue}{\left(1 - t\right)}}\right)\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot {\left(e^{1 \cdot \log a}\right)}^{\left(1 - t\right)}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot {\left(e^{\left(-1 \cdot -1\right) \cdot \log a}\right)}^{\left(1 - t\right)}\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot {\left(e^{-1 \cdot \left(-1 \cdot \log a\right)}\right)}^{\left(1 - t\right)}\right)\right) \]

      8. exp-prod N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot e^{\left(-1 \cdot \left(-1 \cdot \log a\right)\right) \cdot \left(1 - t\right)}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot e^{-1 \cdot \left(\left(-1 \cdot \log a\right) \cdot \left(1 - t\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot e^{-1 \cdot \left(\left(\mathsf{neg}\left(\log a\right)\right) \cdot \left(1 - t\right)\right)}\right)\right) \]

      11. log-rec N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b} \cdot e^{-1 \cdot \left(\log \left(\frac{1}{a}\right) \cdot \left(1 - t\right)\right)}\right)\right) \]

      12. prod-exp N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b + -1 \cdot \left(\log \left(\frac{1}{a}\right) \cdot \left(1 - t\right)\right)}\right)\right) \]

      13. log-rec N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b + -1 \cdot \left(\left(\mathsf{neg}\left(\log a\right)\right) \cdot \left(1 - t\right)\right)}\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b + -1 \cdot \left(\left(-1 \cdot \log a\right) \cdot \left(1 - t\right)\right)}\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(e^{b + \left(-1 \cdot \left(-1 \cdot \log a\right)\right) \cdot \left(1 - t\right)}\right)\right) \]

   7. Simplified 72.9%

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

      1. unpow-prod-up N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left({a}^{t} \cdot \color{blue}{{a}^{-1}}\right)\right)\right) \]

      2. unpow-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left({a}^{t} \cdot \frac{1}{\color{blue}{a}}\right)\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \left(\frac{{a}^{t}}{\color{blue}{a}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{/.f64}\left(\left({a}^{t}\right), \color{blue}{a}\right)\right)\right) \]

      5. pow-lowering-pow.f64 73.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{exp.f64}\left(b\right), \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), a\right)\right)\right) \]

   9. Applied egg-rr 73.0%

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

   10. Taylor expanded in x around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {a}^{t}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({a}^{t}\right)\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right) \]

       3. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \left(a \cdot \left(y \cdot e^{b}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

       5. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

       9. exp-lowering-exp.f64 81.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(a, t\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   12. Simplified 81.0%

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

   if 8.3999999999999996e112 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 65.1%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 87.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 87.7%

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

Alternative 4: 75.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -11:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-105}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{{z}^{y}}}}{a}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -11.0)
   (/ x (* y (* a (exp b))))
   (if (<= b 6e-105)
     (/ (/ x (/ y (pow z y))) a)
     (if (<= b 4.2e+18) (/ (* x (pow a (+ t -1.0))) y) (/ (/ x (exp b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -11.0) {
		tmp = x / (y * (a * exp(b)));
	} else if (b <= 6e-105) {
		tmp = (x / (y / pow(z, y))) / a;
	} else if (b <= 4.2e+18) {
		tmp = (x * pow(a, (t + -1.0))) / 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 <= (-11.0d0)) then
        tmp = x / (y * (a * exp(b)))
    else if (b <= 6d-105) then
        tmp = (x / (y / (z ** y))) / a
    else if (b <= 4.2d+18) then
        tmp = (x * (a ** (t + (-1.0d0)))) / 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 <= -11.0) {
		tmp = x / (y * (a * Math.exp(b)));
	} else if (b <= 6e-105) {
		tmp = (x / (y / Math.pow(z, y))) / a;
	} else if (b <= 4.2e+18) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -11.0:
		tmp = x / (y * (a * math.exp(b)))
	elif b <= 6e-105:
		tmp = (x / (y / math.pow(z, y))) / a
	elif b <= 4.2e+18:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = (x / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -11.0)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	elseif (b <= 6e-105)
		tmp = Float64(Float64(x / Float64(y / (z ^ y))) / a);
	elseif (b <= 4.2e+18)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(x / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -11.0)
		tmp = x / (y * (a * exp(b)));
	elseif (b <= 6e-105)
		tmp = (x / (y / (z ^ y))) / a;
	elseif (b <= 4.2e+18)
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = (x / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -11.0], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-105], N[(N[(x / N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 4.2e+18], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -11

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. exp-diff N/A

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

      3. associate-/l/ N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. div-exp N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. rem-exp-log N/A

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

      11. associate-/r* N/A

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

      12. associate-/l* N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      15. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \left(a \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot e^{b}\right)}\right)\right) \]

   5. Simplified 79.3%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 91.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   8. Simplified 91.5%

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

   if -11 < b < 6.0000000000000002e-105

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 73.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), \color{blue}{a}\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{\frac{y}{{z}^{y}}}\right), a\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{\frac{y}{{z}^{y}}}\right), a\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{{z}^{y}}\right)\right), a\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \left({z}^{y}\right)\right)\right), a\right) \]

      6. pow-lowering-pow.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{pow.f64}\left(z, y\right)\right)\right), a\right) \]

   10. Applied egg-rr 73.7%

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

   if 6.0000000000000002e-105 < b < 4.2e18

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 84.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 84.6%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot x\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), x\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), x\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), x\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), x\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), x\right), y\right) \]

      7. +-lowering-+.f64 82.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), x\right), y\right) \]

   8. Simplified 82.2%

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

   if 4.2e18 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 80.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 80.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 80.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 80.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -11:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-105}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{{z}^{y}}}}{a}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -10:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -10.0)
   (/ x (* y (* a (exp b))))
   (if (<= b 1.45e-106)
     (/ (* x (/ (pow z y) y)) a)
     (if (<= b 9e+18) (/ (* x (pow a (+ t -1.0))) y) (/ (/ x (exp b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -10.0) {
		tmp = x / (y * (a * exp(b)));
	} else if (b <= 1.45e-106) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else if (b <= 9e+18) {
		tmp = (x * pow(a, (t + -1.0))) / 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 <= (-10.0d0)) then
        tmp = x / (y * (a * exp(b)))
    else if (b <= 1.45d-106) then
        tmp = (x * ((z ** y) / y)) / a
    else if (b <= 9d+18) then
        tmp = (x * (a ** (t + (-1.0d0)))) / 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 <= -10.0) {
		tmp = x / (y * (a * Math.exp(b)));
	} else if (b <= 1.45e-106) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else if (b <= 9e+18) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -10.0:
		tmp = x / (y * (a * math.exp(b)))
	elif b <= 1.45e-106:
		tmp = (x * (math.pow(z, y) / y)) / a
	elif b <= 9e+18:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = (x / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -10.0)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	elseif (b <= 1.45e-106)
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	elseif (b <= 9e+18)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(x / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -10.0)
		tmp = x / (y * (a * exp(b)));
	elseif (b <= 1.45e-106)
		tmp = (x * ((z ^ y) / y)) / a;
	elseif (b <= 9e+18)
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = (x / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -10.0], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-106], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 9e+18], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -10

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. exp-diff N/A

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

      3. associate-/l/ N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. div-exp N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. rem-exp-log N/A

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

      11. associate-/r* N/A

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

      12. associate-/l* N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      15. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \left(a \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot e^{b}\right)}\right)\right) \]

   5. Simplified 79.3%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 91.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   8. Simplified 91.5%

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

   if -10 < b < 1.45e-106

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 73.7%

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

   if 1.45e-106 < b < 9e18

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(\log a \cdot \left(t - 1\right) - b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log a \cdot \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\log a, \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t - 1\right)\right), b\right)\right)\right), y\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), b\right)\right)\right), y\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \left(t + -1\right)\right), b\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 84.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), \mathsf{+.f64}\left(t, -1\right)\right), b\right)\right)\right), y\right) \]

   5. Simplified 84.6%

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

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot e^{\log a \cdot \left(t - 1\right)}\right)}, y\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)} \cdot x\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), x\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{\left(t - 1\right)}\right), x\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), x\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), x\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), x\right), y\right) \]

      7. +-lowering-+.f64 82.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), x\right), y\right) \]

   8. Simplified 82.2%

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

   if 9e18 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 80.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 80.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 80.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 80.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -10:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -0.0072:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-285}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 0.52:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -0.0072)
     t_1
     (if (<= b -6.6e-285)
       (/ (* x (* b (* b (* b -0.16666666666666666)))) y)
       (if (<= b 0.52) (/ x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -0.0072) {
		tmp = t_1;
	} else if (b <= -6.6e-285) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 0.52) {
		tmp = x / (y * a);
	} 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 / exp(b)) / y
    if (b <= (-0.0072d0)) then
        tmp = t_1
    else if (b <= (-6.6d-285)) then
        tmp = (x * (b * (b * (b * (-0.16666666666666666d0))))) / y
    else if (b <= 0.52d0) then
        tmp = x / (y * a)
    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.exp(b)) / y;
	double tmp;
	if (b <= -0.0072) {
		tmp = t_1;
	} else if (b <= -6.6e-285) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 0.52) {
		tmp = x / (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -0.0072:
		tmp = t_1
	elif b <= -6.6e-285:
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y
	elif b <= 0.52:
		tmp = x / (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -0.0072)
		tmp = t_1;
	elseif (b <= -6.6e-285)
		tmp = Float64(Float64(x * Float64(b * Float64(b * Float64(b * -0.16666666666666666)))) / y);
	elseif (b <= 0.52)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -0.0072)
		tmp = t_1;
	elseif (b <= -6.6e-285)
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	elseif (b <= 0.52)
		tmp = x / (y * a);
	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[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -0.0072], t$95$1, If[LessEqual[b, -6.6e-285], N[(N[(x * N[(b * N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 0.52], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0071999999999999998 or 0.52000000000000002 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 81.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 81.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 81.3%

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

   if -0.0071999999999999998 < b < -6.5999999999999997e-285

   1. Initial program 96.3%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 10.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 10.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      10. *-lowering-*.f64 10.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 10.5%

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

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right) \cdot {b}^{3}\right)\right), y\right) \]

       4. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{6} \cdot {b}^{3}\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3} \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       8. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \frac{-1}{6}\right)\right), y\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left({b}^{2} \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\left(b \cdot b\right) \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       13. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 42.1%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), y\right) \]

   11. Simplified 42.1%

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

   if -6.5999999999999997e-285 < b < 0.52000000000000002

   1. Initial program 95.9%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 80.4%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 77.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 77.1%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 43.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 43.7%

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

Alternative 7: 73.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{if}\;y \leq -120:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) y)) a)))
   (if (<= y -120.0) t_1 (if (<= y 4.7e+117) (/ x (* y (* a (exp b)))) 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)) / a;
	double tmp;
	if (y <= -120.0) {
		tmp = t_1;
	} else if (y <= 4.7e+117) {
		tmp = x / (y * (a * exp(b)));
	} 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)) / a
    if (y <= (-120.0d0)) then
        tmp = t_1
    else if (y <= 4.7d+117) then
        tmp = x / (y * (a * exp(b)))
    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)) / a;
	double tmp;
	if (y <= -120.0) {
		tmp = t_1;
	} else if (y <= 4.7e+117) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / y)) / a
	tmp = 0
	if y <= -120.0:
		tmp = t_1
	elif y <= 4.7e+117:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / y)) / a)
	tmp = 0.0
	if (y <= -120.0)
		tmp = t_1;
	elseif (y <= 4.7e+117)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	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)) / a;
	tmp = 0.0;
	if (y <= -120.0)
		tmp = t_1;
	elseif (y <= 4.7e+117)
		tmp = x / (y * (a * exp(b)));
	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[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -120.0], t$95$1, If[LessEqual[y, 4.7e+117], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -120 or 4.70000000000000006e117 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 87.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 87.6%

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

   if -120 < y < 4.70000000000000006e117

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. exp-diff N/A

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

      3. associate-/l/ N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. div-exp N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. rem-exp-log N/A

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

      11. associate-/r* N/A

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

      12. associate-/l* N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      15. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \left(a \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot e^{b}\right)}\right)\right) \]

   5. Simplified 70.2%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 72.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   8. Simplified 72.7%

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

Alternative 8: 74.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -3.2e+89) t_1 (if (<= t 5.2e+41) (/ x (* y (* a (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -3.2e+89) {
		tmp = t_1;
	} else if (t <= 5.2e+41) {
		tmp = x / (y * (a * exp(b)));
	} 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 * ((a ** t) / y)
    if (t <= (-3.2d+89)) then
        tmp = t_1
    else if (t <= 5.2d+41) then
        tmp = x / (y * (a * exp(b)))
    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(a, t) / y);
	double tmp;
	if (t <= -3.2e+89) {
		tmp = t_1;
	} else if (t <= 5.2e+41) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -3.2e+89:
		tmp = t_1
	elif t <= 5.2e+41:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -3.2e+89)
		tmp = t_1;
	elseif (t <= 5.2e+41)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -3.2e+89)
		tmp = t_1;
	elseif (t <= 5.2e+41)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+89], t$95$1, If[LessEqual[t, 5.2e+41], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999987e89 or 5.2000000000000001e41 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot \log a\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\log a \cdot t\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\log a, t\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 80.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), t\right)\right)\right), y\right) \]

   5. Simplified 80.1%

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

      1. exp-to-pow N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{a}^{t}}{y}\right), \color{blue}{x}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left({a}^{t}\right), y\right), x\right) \]

      6. pow-lowering-pow.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), y\right), x\right) \]

   7. Applied egg-rr 80.1%

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

   if -3.19999999999999987e89 < t < 5.2000000000000001e41

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. exp-diff N/A

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

      3. associate-/l/ N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. div-exp N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. rem-exp-log N/A

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

      11. associate-/r* N/A

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

      12. associate-/l* N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {z}^{y}\right), \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({z}^{y}\right)\right), \left(\color{blue}{a} \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      15. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \left(a \cdot \left(y \cdot e^{b}\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{pow.f64}\left(z, y\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot e^{b}\right)}\right)\right) \]

   5. Simplified 77.1%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot \left(y \cdot e^{b}\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(y \cdot e^{b}\right) \cdot \color{blue}{a}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\left(e^{b} \cdot a\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \left(a \cdot \color{blue}{e^{b}}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(a \cdot e^{b}\right)}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{\left(e^{b}\right)}\right)\right)\right) \]

      7. exp-lowering-exp.f64 68.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right)\right) \]

   8. Simplified 68.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -11.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -11.2) t_1 (if (<= b 8.4e+18) (/ (* x (pow a t)) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -11.2) {
		tmp = t_1;
	} else if (b <= 8.4e+18) {
		tmp = (x * pow(a, t)) / 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 / exp(b)) / y
    if (b <= (-11.2d0)) then
        tmp = t_1
    else if (b <= 8.4d+18) then
        tmp = (x * (a ** t)) / 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.exp(b)) / y;
	double tmp;
	if (b <= -11.2) {
		tmp = t_1;
	} else if (b <= 8.4e+18) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -11.2:
		tmp = t_1
	elif b <= 8.4e+18:
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -11.2)
		tmp = t_1;
	elseif (b <= 8.4e+18)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -11.2)
		tmp = t_1;
	elseif (b <= 8.4e+18)
		tmp = (x * (a ^ t)) / 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[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -11.2], t$95$1, If[LessEqual[b, 8.4e+18], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -11.199999999999999 or 8.4e18 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 85.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 85.3%

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

   if -11.199999999999999 < b < 8.4e18

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot \log a\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\log a \cdot t\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\log a, t\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 48.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), t\right)\right)\right), y\right) \]

   5. Simplified 48.5%

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

      1. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot {a}^{t}\right), y\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left({a}^{t} \cdot x\right), y\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({a}^{t}\right), x\right), y\right) \]

      4. pow-lowering-pow.f64 48.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(a, t\right), x\right), y\right) \]

   7. Applied egg-rr 48.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -11.2:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -11.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -11.2) t_1 (if (<= b 4.3e+18) (* x (/ (pow a t) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / exp(b)) / y;
	double tmp;
	if (b <= -11.2) {
		tmp = t_1;
	} else if (b <= 4.3e+18) {
		tmp = x * (pow(a, t) / 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 / exp(b)) / y
    if (b <= (-11.2d0)) then
        tmp = t_1
    else if (b <= 4.3d+18) then
        tmp = x * ((a ** t) / 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.exp(b)) / y;
	double tmp;
	if (b <= -11.2) {
		tmp = t_1;
	} else if (b <= 4.3e+18) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -11.2:
		tmp = t_1
	elif b <= 4.3e+18:
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -11.2)
		tmp = t_1;
	elseif (b <= 4.3e+18)
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -11.2)
		tmp = t_1;
	elseif (b <= 4.3e+18)
		tmp = x * ((a ^ t) / 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[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -11.2], t$95$1, If[LessEqual[b, 4.3e+18], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -11.199999999999999 or 4.3e18 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 85.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 85.3%

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

   if -11.199999999999999 < b < 4.3e18

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot \log a\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\log a \cdot t\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\log a, t\right)\right)\right), y\right) \]

      3. log-lowering-log.f64 48.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\mathsf{log.f64}\left(a\right), t\right)\right)\right), y\right) \]

   5. Simplified 48.5%

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

      1. exp-to-pow N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{{a}^{t}}{y}\right), \color{blue}{x}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left({a}^{t}\right), y\right), x\right) \]

      6. pow-lowering-pow.f64 47.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, t\right), y\right), x\right) \]

   7. Applied egg-rr 47.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -11.2:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.6% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-283}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.75e-283)
   (/ (* x (* b (* b (* b -0.16666666666666666)))) y)
   (if (<= b 9e+108)
     (/ x (* y a))
     (/
      (/ x (+ 1.0 (* b (+ 1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e-283) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 9e+108) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.75d-283)) then
        tmp = (x * (b * (b * (b * (-0.16666666666666666d0))))) / y
    else if (b <= 9d+108) then
        tmp = x / (y * a)
    else
        tmp = (x / (1.0d0 + (b * (1.0d0 + (b * (0.5d0 + (b * 0.16666666666666666d0))))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.75e-283) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 9e+108) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.75e-283:
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y
	elif b <= 9e+108:
		tmp = x / (y * a)
	else:
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.75e-283)
		tmp = Float64(Float64(x * Float64(b * Float64(b * Float64(b * -0.16666666666666666)))) / y);
	elseif (b <= 9e+108)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.75e-283)
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	elseif (b <= 9e+108)
		tmp = x / (y * a);
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * (0.5 + (b * 0.16666666666666666))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.75e-283], N[(N[(x * N[(b * N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 9e+108], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7499999999999999e-283

   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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 50.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 50.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      10. *-lowering-*.f64 42.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 42.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right) \cdot {b}^{3}\right)\right), y\right) \]

       4. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{6} \cdot {b}^{3}\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3} \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       8. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \frac{-1}{6}\right)\right), y\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left({b}^{2} \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\left(b \cdot b\right) \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       13. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 58.3%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), y\right) \]

   11. Simplified 58.3%

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

   if -1.7499999999999999e-283 < b < 9e108

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 66.2%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 35.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 35.0%

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

   if 9e108 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 93.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 93.0%

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

Alternative 12: 48.9% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e-284)
   (/ (* x (* b (* b (* b -0.16666666666666666)))) y)
   (if (<= b 9e+108)
     (/ x (* y a))
     (/ (/ x (+ 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 <= -2.5e-284) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 9e+108) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (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 <= (-2.5d-284)) then
        tmp = (x * (b * (b * (b * (-0.16666666666666666d0))))) / y
    else if (b <= 9d+108) then
        tmp = x / (y * a)
    else
        tmp = (x / (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 <= -2.5e-284) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 9e+108) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e-284:
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y
	elif b <= 9e+108:
		tmp = x / (y * a)
	else:
		tmp = (x / (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 <= -2.5e-284)
		tmp = Float64(Float64(x * Float64(b * Float64(b * Float64(b * -0.16666666666666666)))) / y);
	elseif (b <= 9e+108)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / 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 <= -2.5e-284)
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	elseif (b <= 9e+108)
		tmp = x / (y * a);
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e-284], N[(N[(x * N[(b * N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 9e+108], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.49999999999999987e-284

   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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 50.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 50.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      10. *-lowering-*.f64 42.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 42.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right) \cdot {b}^{3}\right)\right), y\right) \]

       4. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{6} \cdot {b}^{3}\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3} \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       8. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \frac{-1}{6}\right)\right), y\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left({b}^{2} \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\left(b \cdot b\right) \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       13. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 58.3%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), y\right) \]

   11. Simplified 58.3%

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

   if -2.49999999999999987e-284 < b < 9e108

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 66.2%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 35.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 35.0%

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

   if 9e108 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 93.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      5. *-lowering-*.f64 86.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 86.1%

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

Alternative 13: 42.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-286}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e-286)
   (/ (* x (* b (* b (* b -0.16666666666666666)))) y)
   (if (<= b 1.45e+109) (/ x (* y a)) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e-286) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 1.45e+109) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.1d-286)) then
        tmp = (x * (b * (b * (b * (-0.16666666666666666d0))))) / y
    else if (b <= 1.45d+109) then
        tmp = x / (y * a)
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e-286) {
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	} else if (b <= 1.45e+109) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.1e-286:
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y
	elif b <= 1.45e+109:
		tmp = x / (y * a)
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e-286)
		tmp = Float64(Float64(x * Float64(b * Float64(b * Float64(b * -0.16666666666666666)))) / y);
	elseif (b <= 1.45e+109)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.1e-286)
		tmp = (x * (b * (b * (b * -0.16666666666666666)))) / y;
	elseif (b <= 1.45e+109)
		tmp = x / (y * a);
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e-286], N[(N[(x * N[(b * N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.45e+109], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.09999999999999988e-286

   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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 50.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 50.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}\right), y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)\right)\right), y\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + -1\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(-1 + b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right), y\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right), y\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right)\right)\right)\right), y\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

      10. *-lowering-*.f64 42.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 42.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right) \cdot {b}^{3}\right)\right), y\right) \]

       4. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left(\frac{1}{6} \cdot {b}^{3}\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\mathsf{neg}\left({b}^{3} \cdot \frac{1}{6}\right)\right)\right), y\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left({b}^{3} \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       8. cube-mult N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       9. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \left(\mathsf{neg}\left(\frac{1}{6}\right)\right)\right)\right), y\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(b \cdot {b}^{2}\right) \cdot \frac{-1}{6}\right)\right), y\right) \]

       11. associate-*l* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left({b}^{2} \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\left(b \cdot b\right) \cdot \frac{-1}{6}\right)\right)\right), y\right) \]

       13. associate-*r* N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       14. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       16. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), y\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), y\right) \]

       18. *-lowering-*.f64 58.3%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), y\right) \]

   11. Simplified 58.3%

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

   if -2.09999999999999988e-286 < b < 1.45e109

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 66.2%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 35.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 35.0%

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

   if 1.45e109 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 93.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 40.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 40.7%

       \[\leadsto \frac{\frac{x}{\color{blue}{b + 1}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-286}:\\ \;\;\;\;\frac{x \cdot \left(b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-284}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e-284)
   (/ (* 0.5 (* x (* b b))) y)
   (if (<= b 4e+110) (/ x (* y a)) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e-284) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else if (b <= 4e+110) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d-284)) then
        tmp = (0.5d0 * (x * (b * b))) / y
    else if (b <= 4d+110) then
        tmp = x / (y * a)
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e-284) {
		tmp = (0.5 * (x * (b * b))) / y;
	} else if (b <= 4e+110) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e-284:
		tmp = (0.5 * (x * (b * b))) / y
	elif b <= 4e+110:
		tmp = x / (y * a)
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e-284)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / y);
	elseif (b <= 4e+110)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e-284)
		tmp = (0.5 * (x * (b * b))) / y;
	elseif (b <= 4e+110)
		tmp = x / (y * a);
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e-284], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4e+110], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.80000000000000006e-284

   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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 50.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 50.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(b \cdot \left(-1 \cdot \frac{x}{y} + \frac{1}{2} \cdot \frac{b \cdot x}{y}\right)\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(-1 \cdot \frac{x}{y} + \frac{1}{2} \cdot \frac{b \cdot x}{y}\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(b \cdot \left(\frac{1}{2} \cdot \frac{b \cdot x}{y} + \color{blue}{-1 \cdot \frac{x}{y}}\right)\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(b \cdot \left(\frac{1}{2} \cdot \left(b \cdot \frac{x}{y}\right) + -1 \cdot \frac{x}{y}\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(b \cdot \left(\left(\frac{1}{2} \cdot b\right) \cdot \frac{x}{y} + \color{blue}{-1} \cdot \frac{x}{y}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(b \cdot \left(\left(b \cdot \frac{1}{2}\right) \cdot \frac{x}{y} + -1 \cdot \frac{x}{y}\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(b \cdot \left(b \cdot \left(\frac{1}{2} \cdot \frac{x}{y}\right) + \color{blue}{-1} \cdot \frac{x}{y}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(b \cdot \left(\frac{1}{2} \cdot \frac{x}{y}\right) + -1 \cdot \frac{x}{y}\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \frac{x}{y}\right) + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \frac{x}{y}\right) - \color{blue}{\frac{x}{y}}\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \frac{x}{y}\right)\right), \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

   8. Simplified 33.8%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right), \color{blue}{y}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2} \cdot x\right)\right), y\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(x \cdot {b}^{2}\right)\right), y\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left({b}^{2}\right)\right)\right), y\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \left(b \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 55.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   11. Simplified 55.1%

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

   if -4.80000000000000006e-284 < b < 4.0000000000000001e110

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 66.2%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 35.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 35.0%

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

   if 4.0000000000000001e110 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 93.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 40.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 40.7%

       \[\leadsto \frac{\frac{x}{\color{blue}{b + 1}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-284}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+79)
   (/ (* x (- 1.0 b)) y)
   (if (<= b 1.8e+113) (/ x (* y a)) (/ (/ x (+ 1.0 b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+79) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 1.8e+113) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.8d+79)) then
        tmp = (x * (1.0d0 - b)) / y
    else if (b <= 1.8d+113) then
        tmp = x / (y * a)
    else
        tmp = (x / (1.0d0 + b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+79) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 1.8e+113) {
		tmp = x / (y * a);
	} else {
		tmp = (x / (1.0 + b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.8e+79:
		tmp = (x * (1.0 - b)) / y
	elif b <= 1.8e+113:
		tmp = x / (y * a)
	else:
		tmp = (x / (1.0 + b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+79)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	elseif (b <= 1.8e+113)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(1.0 + b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.8e+79)
		tmp = (x * (1.0 - b)) / y;
	elseif (b <= 1.8e+113)
		tmp = x / (y * a);
	else
		tmp = (x / (1.0 + b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+79], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.8e+113], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8000000000000001e79

   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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + -1 \cdot \left(b \cdot x\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(-1 \cdot b\right) \cdot x\right), y\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(b\right)\right) \cdot x\right), y\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right) \cdot x\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right) \cdot x\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right), x\right), y\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - b\right), x\right), y\right) \]

      7. --lowering--.f64 46.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 46.4%

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

   if -2.8000000000000001e79 < b < 1.79999999999999996e113

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 72.0%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 64.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 64.9%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 34.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 34.8%

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

   if 1.79999999999999996e113 < 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. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{e^{0}}{e^{b}}\right), y\right) \]

      2. 1-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      5. exp-lowering-exp.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 93.0%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(1 + b\right)}\right), y\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(b + 1\right)\right), y\right) \]

      2. +-lowering-+.f64 40.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 40.7%

       \[\leadsto \frac{\frac{x}{\color{blue}{b + 1}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.5% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{\frac{1}{y}}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 5.6e-34) (/ x (* y a)) (* x (* y (/ (/ 1.0 y) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.6e-34) {
		tmp = x / (y * a);
	} else {
		tmp = x * (y * ((1.0 / y) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 5.6d-34) then
        tmp = x / (y * a)
    else
        tmp = x * (y * ((1.0d0 / y) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.6e-34) {
		tmp = x / (y * a);
	} else {
		tmp = x * (y * ((1.0 / y) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 5.6e-34:
		tmp = x / (y * a)
	else:
		tmp = x * (y * ((1.0 / y) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 5.6e-34)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x * Float64(y * Float64(Float64(1.0 / y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 5.6e-34)
		tmp = x / (y * a);
	else
		tmp = x * (y * ((1.0 / y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 5.6e-34], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(N[(1.0 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.59999999999999994e-34

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 62.4%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 62.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 62.0%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 37.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 37.6%

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

   if 5.59999999999999994e-34 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 44.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 44.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, y\right) \]
   7. Step-by-step derivation

   8. Simplified 11.7%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 11.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, y\right), x\right) \]

   10. Applied egg-rr 11.7%

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

       1. inv-pow N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{-1}\right), x\right) \]

       2. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{\left(-2 - -1\right)}\right), x\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{\left(\left(\mathsf{neg}\left(2\right)\right) - -1\right)}\right), x\right) \]

       4. pow-div N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{{y}^{\left(\mathsf{neg}\left(2\right)\right)}}{{y}^{-1}}\right), x\right) \]

       5. pow-flip N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{{y}^{2}}}{{y}^{-1}}\right), x\right) \]

       6. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{y \cdot y}}{{y}^{-1}}\right), x\right) \]

       7. inv-pow N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{y \cdot y}}{\frac{1}{y}}\right), x\right) \]

       8. div-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y \cdot y} \cdot \frac{1}{\frac{1}{y}}\right), x\right) \]

       9. clear-num N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y \cdot y} \cdot \frac{y}{1}\right), x\right) \]

       10. /-rgt-identity N/A

           \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{y \cdot y} \cdot y\right), x\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{y \cdot y}\right), y\right), x\right) \]

       12. associate-/r* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{1}{y}}{y}\right), y\right), x\right) \]

       13. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{y}\right), y\right), y\right), x\right) \]

       14. /-lowering-/.f64 34.2%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), y\right), y\right), x\right) \]

   12. Applied egg-rr 34.2%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{\frac{1}{y}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.0% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+77) (/ (* x (- 1.0 b)) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+77) {
		tmp = (x * (1.0 - b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.5d+77)) then
        tmp = (x * (1.0d0 - b)) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+77) {
		tmp = (x * (1.0 - b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+77:
		tmp = (x * (1.0 - b)) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+77)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.5e+77)
		tmp = (x * (1.0 - b)) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+77], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5e77

   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 b around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

      3. --lowering--.f64 93.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 93.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + -1 \cdot \left(b \cdot x\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(-1 \cdot b\right) \cdot x\right), y\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(b\right)\right) \cdot x\right), y\right) \]

      3. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\left(\mathsf{neg}\left(b\right)\right) + 1\right) \cdot x\right), y\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right) \cdot x\right), y\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + \left(\mathsf{neg}\left(b\right)\right)\right), x\right), y\right) \]

      6. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - b\right), x\right), y\right) \]

      7. --lowering--.f64 46.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 46.4%

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

   if -6.5e77 < b

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

   5. Simplified 65.0%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

      7. pow-lowering-pow.f64 59.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

   8. Simplified 59.9%

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

   9. Taylor expanded in y around 0

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

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

       3. *-lowering-*.f64 31.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 31.9%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.3% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

3. Taylor expanded in b around 0

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

5. Simplified 61.3%

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

6. Taylor expanded in t around 0

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

   1. *-commutative N/A

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

   2. associate-/r* N/A

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

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot {z}^{y}}{y}\right), \color{blue}{a}\right) \]

   4. associate-/l* N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{{z}^{y}}{y}\right), a\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{{z}^{y}}{y}\right)\right), a\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({z}^{y}\right), y\right)\right), a\right) \]

   7. pow-lowering-pow.f64 57.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(z, y\right), y\right)\right), a\right) \]

8. Simplified 57.6%

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

9. Taylor expanded in y around 0

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

    1. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

    2. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{a}\right)\right) \]

    3. *-lowering-*.f64 30.5%

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{a}\right)\right) \]

11. Simplified 30.5%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
12. Add Preprocessing

Alternative 19: 15.5% 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 98.1%

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

3. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot b\right)}\right)\right), y\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(b\right)\right)\right)\right), y\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\left(0 - b\right)\right)\right), y\right) \]

   3. --lowering--.f64 48.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 48.0%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, y\right) \]
7. Step-by-step derivation

8. Simplified 12.4%

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

Developer Target 1: 71.9% 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 2024191 
(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))