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

Percentage Accurate: 98.4% → 98.4%

Time: 16.4s

Alternatives: 26

Speedup: 1.0×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 82.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -5200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -5200.0)
     t_1
     (if (<= b 1.3e+53) (* x (* (pow a (+ t -1.0)) (/ (pow z y) 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 <= -5200.0) {
		tmp = t_1;
	} else if (b <= 1.3e+53) {
		tmp = x * (pow(a, (t + -1.0)) * (pow(z, y) / 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 <= (-5200.0d0)) then
        tmp = t_1
    else if (b <= 1.3d+53) then
        tmp = x * ((a ** (t + (-1.0d0))) * ((z ** y) / 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 <= -5200.0) {
		tmp = t_1;
	} else if (b <= 1.3e+53) {
		tmp = x * (Math.pow(a, (t + -1.0)) * (Math.pow(z, y) / 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 <= -5200.0:
		tmp = t_1
	elif b <= 1.3e+53:
		tmp = x * (math.pow(a, (t + -1.0)) * (math.pow(z, y) / 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 <= -5200.0)
		tmp = t_1;
	elseif (b <= 1.3e+53)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) * Float64((z ^ y) / 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 <= -5200.0)
		tmp = t_1;
	elseif (b <= 1.3e+53)
		tmp = x * ((a ^ (t + -1.0)) * ((z ^ y) / 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, -5200.0], t$95$1, If[LessEqual[b, 1.3e+53], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5200 or 1.29999999999999999e53 < 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 87.9%

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

   5. Simplified 87.9%

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

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

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

      2. sub0-neg N/A

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

      3. rec-exp N/A

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

      4. un-div-inv N/A

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

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

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

      6. exp-lowering-exp.f64 87.9%

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

   7. Applied egg-rr 87.9%

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

   if -5200 < b < 1.29999999999999999e53

   1. Initial program 97.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

   4. Applied egg-rr 83.3%

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

   5. Taylor expanded in b around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

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

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

      9. pow-lowering-pow.f64 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5200:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{z}^{y}}}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8000000000:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow z y)))))
   (if (<= y -1.5e+150)
     t_1
     (if (<= y 8000000000.0) (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(z, y));
	double tmp;
	if (y <= -1.5e+150) {
		tmp = t_1;
	} else if (y <= 8000000000.0) {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y / (z ** y))
    if (y <= (-1.5d+150)) then
        tmp = t_1
    else if (y <= 8000000000.0d0) then
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / Math.pow(z, y));
	double tmp;
	if (y <= -1.5e+150) {
		tmp = t_1;
	} else if (y <= 8000000000.0) {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(z, y))
	tmp = 0
	if y <= -1.5e+150:
		tmp = t_1
	elif y <= 8000000000.0:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (z ^ y)))
	tmp = 0.0
	if (y <= -1.5e+150)
		tmp = t_1;
	elseif (y <= 8000000000.0)
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (z ^ y));
	tmp = 0.0;
	if (y <= -1.5e+150)
		tmp = t_1;
	elseif (y <= 8000000000.0)
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+150], t$95$1, If[LessEqual[y, 8000000000.0], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000006e150 or 8e9 < 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 89.6%

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

   5. Simplified 89.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. pow-lowering-pow.f64 89.6%

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

   7. Applied egg-rr 89.6%

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

   if -1.50000000000000006e150 < y < 8e9

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 85.0%

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

   5. Simplified 85.0%

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

Alternative 4: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -1.18e+83)
     t_1
     (if (<= t 3e+81) (* x (/ (pow z y) (* a (* y (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 <= -1.18e+83) {
		tmp = t_1;
	} else if (t <= 3e+81) {
		tmp = x * (pow(z, y) / (a * (y * 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 <= (-1.18d+83)) then
        tmp = t_1
    else if (t <= 3d+81) then
        tmp = x * ((z ** y) / (a * (y * 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 <= -1.18e+83) {
		tmp = t_1;
	} else if (t <= 3e+81) {
		tmp = x * (Math.pow(z, y) / (a * (y * 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 <= -1.18e+83:
		tmp = t_1
	elif t <= 3e+81:
		tmp = x * (math.pow(z, y) / (a * (y * 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 <= -1.18e+83)
		tmp = t_1;
	elseif (t <= 3e+81)
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * 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 <= -1.18e+83)
		tmp = t_1;
	elseif (t <= 3e+81)
		tmp = x * ((z ^ y) / (a * (y * 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, -1.18e+83], t$95$1, If[LessEqual[t, 3e+81], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1799999999999999e83 or 2.99999999999999997e81 < 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 82.0%

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

   5. Simplified 82.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 82.0%

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

   7. Applied egg-rr 82.0%

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

   if -1.1799999999999999e83 < t < 2.99999999999999997e81

   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. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\right)}, x\right) \]
   6. Step-by-step derivation

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

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

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

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

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

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

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

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

      5. exp-lowering-exp.f64 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{z}^{y}}}\\ t_2 := x \cdot \frac{{a}^{t}}{y}\\ t_3 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -115000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{a \cdot \left(y \cdot \left(1 + b\right)\right)}{x}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-260}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow z y))))
        (t_2 (* x (/ (pow a t) y)))
        (t_3 (/ (/ x (exp b)) y)))
   (if (<= b -115000000000.0)
     t_3
     (if (<= b -3.6e-103)
       t_1
       (if (<= b -1.6e-302)
         (/ 1.0 (/ (* a (* y (+ 1.0 b))) x))
         (if (<= b 1.05e-260)
           t_2
           (if (<= b 4.5e-98) t_1 (if (<= b 2.05e+23) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(z, y));
	double t_2 = x * (pow(a, t) / y);
	double t_3 = (x / exp(b)) / y;
	double tmp;
	if (b <= -115000000000.0) {
		tmp = t_3;
	} else if (b <= -3.6e-103) {
		tmp = t_1;
	} else if (b <= -1.6e-302) {
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x);
	} else if (b <= 1.05e-260) {
		tmp = t_2;
	} else if (b <= 4.5e-98) {
		tmp = t_1;
	} else if (b <= 2.05e+23) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x / (y / (z ** y))
    t_2 = x * ((a ** t) / y)
    t_3 = (x / exp(b)) / y
    if (b <= (-115000000000.0d0)) then
        tmp = t_3
    else if (b <= (-3.6d-103)) then
        tmp = t_1
    else if (b <= (-1.6d-302)) then
        tmp = 1.0d0 / ((a * (y * (1.0d0 + b))) / x)
    else if (b <= 1.05d-260) then
        tmp = t_2
    else if (b <= 4.5d-98) then
        tmp = t_1
    else if (b <= 2.05d+23) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / Math.pow(z, y));
	double t_2 = x * (Math.pow(a, t) / y);
	double t_3 = (x / Math.exp(b)) / y;
	double tmp;
	if (b <= -115000000000.0) {
		tmp = t_3;
	} else if (b <= -3.6e-103) {
		tmp = t_1;
	} else if (b <= -1.6e-302) {
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x);
	} else if (b <= 1.05e-260) {
		tmp = t_2;
	} else if (b <= 4.5e-98) {
		tmp = t_1;
	} else if (b <= 2.05e+23) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(z, y))
	t_2 = x * (math.pow(a, t) / y)
	t_3 = (x / math.exp(b)) / y
	tmp = 0
	if b <= -115000000000.0:
		tmp = t_3
	elif b <= -3.6e-103:
		tmp = t_1
	elif b <= -1.6e-302:
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x)
	elif b <= 1.05e-260:
		tmp = t_2
	elif b <= 4.5e-98:
		tmp = t_1
	elif b <= 2.05e+23:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (z ^ y)))
	t_2 = Float64(x * Float64((a ^ t) / y))
	t_3 = Float64(Float64(x / exp(b)) / y)
	tmp = 0.0
	if (b <= -115000000000.0)
		tmp = t_3;
	elseif (b <= -3.6e-103)
		tmp = t_1;
	elseif (b <= -1.6e-302)
		tmp = Float64(1.0 / Float64(Float64(a * Float64(y * Float64(1.0 + b))) / x));
	elseif (b <= 1.05e-260)
		tmp = t_2;
	elseif (b <= 4.5e-98)
		tmp = t_1;
	elseif (b <= 2.05e+23)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (z ^ y));
	t_2 = x * ((a ^ t) / y);
	t_3 = (x / exp(b)) / y;
	tmp = 0.0;
	if (b <= -115000000000.0)
		tmp = t_3;
	elseif (b <= -3.6e-103)
		tmp = t_1;
	elseif (b <= -1.6e-302)
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x);
	elseif (b <= 1.05e-260)
		tmp = t_2;
	elseif (b <= 4.5e-98)
		tmp = t_1;
	elseif (b <= 2.05e+23)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -115000000000.0], t$95$3, If[LessEqual[b, -3.6e-103], t$95$1, If[LessEqual[b, -1.6e-302], N[(1.0 / N[(N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-260], t$95$2, If[LessEqual[b, 4.5e-98], t$95$1, If[LessEqual[b, 2.05e+23], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e11 or 2.04999999999999998e23 < 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 86.3%

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

   5. Simplified 86.3%

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

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

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

      2. sub0-neg N/A

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

      3. rec-exp N/A

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

      4. un-div-inv N/A

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

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

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

      6. exp-lowering-exp.f64 86.3%

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

   7. Applied egg-rr 86.3%

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

   if -1.15e11 < b < -3.5999999999999998e-103 or 1.05000000000000002e-260 < b < 4.49999999999999997e-98

   1. Initial program 97.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 68.5%

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

   5. Simplified 68.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. pow-lowering-pow.f64 68.5%

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

   7. Applied egg-rr 68.5%

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

   if -3.5999999999999998e-103 < b < -1.59999999999999989e-302

   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 y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 51.9%

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

   8. Simplified 51.9%

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

      1. clear-num N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. div-inv N/A

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

      6. clear-num N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

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

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

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

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

      17. exp-lowering-exp.f64 57.0%

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

   10. Applied egg-rr 57.0%

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

   11. Taylor expanded in b around 0

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

       1. distribute-lft-out N/A

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

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

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

       3. distribute-rgt1-in N/A

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

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

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

       5. +-lowering-+.f64 57.0%

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

   13. Simplified 57.0%

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

   if -1.59999999999999989e-302 < b < 1.05000000000000002e-260 or 4.49999999999999997e-98 < b < 2.04999999999999998e23

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 81.1%

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

   5. Simplified 81.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 81.1%

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

   7. Applied egg-rr 81.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -115000000000:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y}}}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{a \cdot \left(y \cdot \left(1 + b\right)\right)}{x}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y}}}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{z}^{y}}}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow z y)))))
   (if (<= y -2.7e+131)
     t_1
     (if (<= y 1.02e+35) (/ 1.0 (/ (* y (* a (exp b))) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(z, y));
	double tmp;
	if (y <= -2.7e+131) {
		tmp = t_1;
	} else if (y <= 1.02e+35) {
		tmp = 1.0 / ((y * (a * exp(b))) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y / (z ** y))
    if (y <= (-2.7d+131)) then
        tmp = t_1
    else if (y <= 1.02d+35) then
        tmp = 1.0d0 / ((y * (a * exp(b))) / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / Math.pow(z, y));
	double tmp;
	if (y <= -2.7e+131) {
		tmp = t_1;
	} else if (y <= 1.02e+35) {
		tmp = 1.0 / ((y * (a * Math.exp(b))) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(z, y))
	tmp = 0
	if y <= -2.7e+131:
		tmp = t_1
	elif y <= 1.02e+35:
		tmp = 1.0 / ((y * (a * math.exp(b))) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (z ^ y)))
	tmp = 0.0
	if (y <= -2.7e+131)
		tmp = t_1;
	elseif (y <= 1.02e+35)
		tmp = Float64(1.0 / Float64(Float64(y * Float64(a * exp(b))) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (z ^ y));
	tmp = 0.0;
	if (y <= -2.7e+131)
		tmp = t_1;
	elseif (y <= 1.02e+35)
		tmp = 1.0 / ((y * (a * exp(b))) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+131], t$95$1, If[LessEqual[y, 1.02e+35], N[(1.0 / N[(N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000004e131 or 1.02000000000000007e35 < 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 88.6%

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

   5. Simplified 88.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. pow-lowering-pow.f64 88.6%

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

   7. Applied egg-rr 88.6%

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

   if -2.70000000000000004e131 < y < 1.02000000000000007e35

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 73.2%

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

   8. Simplified 73.2%

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

      1. clear-num N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. div-inv N/A

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

      6. clear-num N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

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

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

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

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

      17. exp-lowering-exp.f64 74.8%

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

   10. Applied egg-rr 74.8%

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

Alternative 7: 72.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{z}^{y}}}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow z y)))))
   (if (<= y -4.3e+131)
     t_1
     (if (<= y 1.55e+35) (/ (/ x (* a (exp b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(z, y));
	double tmp;
	if (y <= -4.3e+131) {
		tmp = t_1;
	} else if (y <= 1.55e+35) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y / (z ** y))
    if (y <= (-4.3d+131)) then
        tmp = t_1
    else if (y <= 1.55d+35) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / Math.pow(z, y));
	double tmp;
	if (y <= -4.3e+131) {
		tmp = t_1;
	} else if (y <= 1.55e+35) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(z, y))
	tmp = 0
	if y <= -4.3e+131:
		tmp = t_1
	elif y <= 1.55e+35:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (z ^ y)))
	tmp = 0.0
	if (y <= -4.3e+131)
		tmp = t_1;
	elseif (y <= 1.55e+35)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (z ^ y));
	tmp = 0.0;
	if (y <= -4.3e+131)
		tmp = t_1;
	elseif (y <= 1.55e+35)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+131], t$95$1, If[LessEqual[y, 1.55e+35], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3000000000000001e131 or 1.54999999999999993e35 < 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 88.6%

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

   5. Simplified 88.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

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

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

      8. pow-lowering-pow.f64 88.6%

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

   7. Applied egg-rr 88.6%

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

   if -4.3000000000000001e131 < y < 1.54999999999999993e35

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 73.2%

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

   8. Simplified 73.2%

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

Alternative 8: 66.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -6.6e+37) t_1 (if (<= b 4e+24) (* 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 <= -6.6e+37) {
		tmp = t_1;
	} else if (b <= 4e+24) {
		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 <= (-6.6d+37)) then
        tmp = t_1
    else if (b <= 4d+24) 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 <= -6.6e+37) {
		tmp = t_1;
	} else if (b <= 4e+24) {
		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 <= -6.6e+37:
		tmp = t_1
	elif b <= 4e+24:
		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 <= -6.6e+37)
		tmp = t_1;
	elseif (b <= 4e+24)
		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 <= -6.6e+37)
		tmp = t_1;
	elseif (b <= 4e+24)
		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, -6.6e+37], t$95$1, If[LessEqual[b, 4e+24], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.6000000000000002e37 or 3.9999999999999999e24 < 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 86.8%

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

   5. Simplified 86.8%

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

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

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

      2. sub0-neg N/A

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

      3. rec-exp N/A

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

      4. un-div-inv N/A

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

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

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

      6. exp-lowering-exp.f64 86.8%

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

   7. Applied egg-rr 86.8%

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

   if -6.6000000000000002e37 < b < 3.9999999999999999e24

   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 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 50.4%

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

   5. Simplified 50.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. exp-to-pow N/A

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

      6. pow-lowering-pow.f64 50.4%

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

   7. Applied egg-rr 50.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{e^{b}}}{y}\\ \mathbf{if}\;b \leq -1.9:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (exp b)) y)))
   (if (<= b -1.9)
     t_1
     (if (<= b 1.55e+23)
       (/
        1.0
        (/
         (*
          y
          (+
           a
           (* b (+ a (* b (+ (* a (* b 0.16666666666666666)) (* a 0.5)))))))
         x))
       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 <= -1.9) {
		tmp = t_1;
	} else if (b <= 1.55e+23) {
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	} 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 <= (-1.9d0)) then
        tmp = t_1
    else if (b <= 1.55d+23) then
        tmp = 1.0d0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666d0)) + (a * 0.5d0))))))) / x)
    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 <= -1.9) {
		tmp = t_1;
	} else if (b <= 1.55e+23) {
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	} 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 <= -1.9:
		tmp = t_1
	elif b <= 1.55e+23:
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x)
	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 <= -1.9)
		tmp = t_1;
	elseif (b <= 1.55e+23)
		tmp = Float64(1.0 / Float64(Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(a * Float64(b * 0.16666666666666666)) + Float64(a * 0.5))))))) / x));
	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 <= -1.9)
		tmp = t_1;
	elseif (b <= 1.55e+23)
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	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, -1.9], t$95$1, If[LessEqual[b, 1.55e+23], N[(1.0 / N[(N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(a * N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8999999999999999 or 1.54999999999999985e23 < 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 86.4%

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

   5. Simplified 86.4%

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

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

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

      2. sub0-neg N/A

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

      3. rec-exp N/A

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

      4. un-div-inv N/A

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

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

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

      6. exp-lowering-exp.f64 86.4%

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

   7. Applied egg-rr 86.4%

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

   if -1.8999999999999999 < b < 1.54999999999999985e23

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 36.7%

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

   8. Simplified 36.7%

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

      1. clear-num N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. div-inv N/A

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

      6. clear-num N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

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

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

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

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

      17. exp-lowering-exp.f64 39.0%

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

   10. Applied egg-rr 39.0%

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

   11. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

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

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

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

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

       10. *-commutative N/A

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

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

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

       12. *-commutative N/A

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

       13. *-lowering-*.f64 40.7%

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

   13. Simplified 40.7%

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

Alternative 10: 52.9% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + a \cdot \left(b \cdot 0.5\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(b \cdot 0.16666666666666666 + 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b (* b b)) -0.16666666666666666)) y)))
   (if (<= b -2.5e-5)
     t_1
     (if (<= b -6.4e-261)
       (/ (/ x (* a (+ 1.0 b))) y)
       (if (<= b 7.4e-104)
         t_1
         (if (<= b 3.6e+48)
           (/ (/ x (+ a (* b (+ a (* a (* b 0.5)))))) y)
           (/
            (/ x (+ 1.0 (* b (+ 1.0 (* b (+ (* b 0.16666666666666666) 0.5))))))
            y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_1;
	} else if (b <= -6.4e-261) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 7.4e-104) {
		tmp = t_1;
	} else if (b <= 3.6e+48) {
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 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) :: t_1
    real(8) :: tmp
    t_1 = (x * ((b * (b * b)) * (-0.16666666666666666d0))) / y
    if (b <= (-2.5d-5)) then
        tmp = t_1
    else if (b <= (-6.4d-261)) then
        tmp = (x / (a * (1.0d0 + b))) / y
    else if (b <= 7.4d-104) then
        tmp = t_1
    else if (b <= 3.6d+48) then
        tmp = (x / (a + (b * (a + (a * (b * 0.5d0)))))) / y
    else
        tmp = (x / (1.0d0 + (b * (1.0d0 + (b * ((b * 0.16666666666666666d0) + 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 t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_1;
	} else if (b <= -6.4e-261) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 7.4e-104) {
		tmp = t_1;
	} else if (b <= 3.6e+48) {
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y;
	} else {
		tmp = (x / (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 0.5)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y
	tmp = 0
	if b <= -2.5e-5:
		tmp = t_1
	elif b <= -6.4e-261:
		tmp = (x / (a * (1.0 + b))) / y
	elif b <= 7.4e-104:
		tmp = t_1
	elif b <= 3.6e+48:
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y
	else:
		tmp = (x / (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 0.5)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * Float64(b * b)) * -0.16666666666666666)) / y)
	tmp = 0.0
	if (b <= -2.5e-5)
		tmp = t_1;
	elseif (b <= -6.4e-261)
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	elseif (b <= 7.4e-104)
		tmp = t_1;
	elseif (b <= 3.6e+48)
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(a * Float64(b * 0.5)))))) / y);
	else
		tmp = Float64(Float64(x / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(Float64(b * 0.16666666666666666) + 0.5)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	tmp = 0.0;
	if (b <= -2.5e-5)
		tmp = t_1;
	elseif (b <= -6.4e-261)
		tmp = (x / (a * (1.0 + b))) / y;
	elseif (b <= 7.4e-104)
		tmp = t_1;
	elseif (b <= 3.6e+48)
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y;
	else
		tmp = (x / (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 0.5)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.5e-5], t$95$1, If[LessEqual[b, -6.4e-261], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.4e-104], t$95$1, If[LessEqual[b, 3.6e+48], N[(N[(x / N[(a + N[(b * N[(a + N[(a * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(1.0 + N[(b * N[(1.0 + N[(b * N[(N[(b * 0.16666666666666666), $MachinePrecision] + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.50000000000000012e-5 or -6.40000000000000008e-261 < b < 7.3999999999999999e-104

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 46.7%

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

   8. Simplified 46.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

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

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. *-commutative N/A

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

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

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

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

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

       11. cube-mult N/A

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

       12. unpow2 N/A

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

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

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

       14. unpow2 N/A

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

       15. *-lowering-*.f64 66.7%

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

   11. Simplified 66.7%

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

   if -2.50000000000000012e-5 < b < -6.40000000000000008e-261

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 47.0%

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

   8. Simplified 47.0%

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

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. distribute-rgt1-in N/A

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

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

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

       4. +-lowering-+.f64 47.0%

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

   11. Simplified 47.0%

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

   if 7.3999999999999999e-104 < b < 3.59999999999999983e48

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 46.0%

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

   8. Simplified 46.0%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

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

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

       6. *-commutative N/A

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

       7. *-commutative N/A

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

       8. associate-*l* N/A

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

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

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

       10. *-commutative N/A

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

       11. *-lowering-*.f64 46.4%

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

   11. Simplified 46.4%

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

   if 3.59999999999999983e48 < 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 82.4%

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

   5. Simplified 82.4%

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

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

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

      2. sub0-neg N/A

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

      3. rec-exp N/A

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

      4. un-div-inv N/A

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

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

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

      6. exp-lowering-exp.f64 82.4%

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

   7. Applied egg-rr 82.4%

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

   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 75.2%

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

   10. Simplified 75.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + a \cdot \left(b \cdot 0.5\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b \cdot \left(1 + b \cdot \left(b \cdot 0.16666666666666666 + 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + a \cdot \left(b \cdot 0.5\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 - b \cdot \left(-1 - b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b (* b b)) -0.16666666666666666)) y)))
   (if (<= b -2.5e-5)
     t_1
     (if (<= b -3.6e-261)
       (/ (/ x (* a (+ 1.0 b))) y)
       (if (<= b 2.7e-107)
         t_1
         (if (<= b 6.1e+153)
           (/ (/ x (+ a (* b (+ a (* a (* b 0.5)))))) y)
           (/ (/ 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 t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_1;
	} else if (b <= -3.6e-261) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 2.7e-107) {
		tmp = t_1;
	} else if (b <= 6.1e+153) {
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * ((b * (b * b)) * (-0.16666666666666666d0))) / y
    if (b <= (-2.5d-5)) then
        tmp = t_1
    else if (b <= (-3.6d-261)) then
        tmp = (x / (a * (1.0d0 + b))) / y
    else if (b <= 2.7d-107) then
        tmp = t_1
    else if (b <= 6.1d+153) then
        tmp = (x / (a + (b * (a + (a * (b * 0.5d0)))))) / y
    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 t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_1;
	} else if (b <= -3.6e-261) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 2.7e-107) {
		tmp = t_1;
	} else if (b <= 6.1e+153) {
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y;
	} else {
		tmp = (x / (1.0 - (b * (-1.0 - (b * 0.5))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y
	tmp = 0
	if b <= -2.5e-5:
		tmp = t_1
	elif b <= -3.6e-261:
		tmp = (x / (a * (1.0 + b))) / y
	elif b <= 2.7e-107:
		tmp = t_1
	elif b <= 6.1e+153:
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y
	else:
		tmp = (x / (1.0 - (b * (-1.0 - (b * 0.5))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * Float64(b * b)) * -0.16666666666666666)) / y)
	tmp = 0.0
	if (b <= -2.5e-5)
		tmp = t_1;
	elseif (b <= -3.6e-261)
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	elseif (b <= 2.7e-107)
		tmp = t_1;
	elseif (b <= 6.1e+153)
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(a * Float64(b * 0.5)))))) / y);
	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)
	t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	tmp = 0.0;
	if (b <= -2.5e-5)
		tmp = t_1;
	elseif (b <= -3.6e-261)
		tmp = (x / (a * (1.0 + b))) / y;
	elseif (b <= 2.7e-107)
		tmp = t_1;
	elseif (b <= 6.1e+153)
		tmp = (x / (a + (b * (a + (a * (b * 0.5)))))) / y;
	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_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.5e-5], t$95$1, If[LessEqual[b, -3.6e-261], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.7e-107], t$95$1, If[LessEqual[b, 6.1e+153], N[(N[(x / N[(a + N[(b * N[(a + N[(a * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $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 4 regimes

2. if b < -2.50000000000000012e-5 or -3.59999999999999999e-261 < b < 2.7e-107

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 46.7%

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

   8. Simplified 46.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

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

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. *-commutative N/A

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

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

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

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

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

       11. cube-mult N/A

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

       12. unpow2 N/A

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

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

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

       14. unpow2 N/A

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

       15. *-lowering-*.f64 66.7%

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

   11. Simplified 66.7%

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

   if -2.50000000000000012e-5 < b < -3.59999999999999999e-261

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 47.0%

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

   8. Simplified 47.0%

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

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. distribute-rgt1-in N/A

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

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

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

       4. +-lowering-+.f64 47.0%

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

   11. Simplified 47.0%

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

   if 2.7e-107 < b < 6.0999999999999998e153

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 61.5%

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

   8. Simplified 61.5%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

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

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

       6. *-commutative N/A

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

       7. *-commutative N/A

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

       8. associate-*l* N/A

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

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

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

       10. *-commutative N/A

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

       11. *-lowering-*.f64 47.8%

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

   11. Simplified 47.8%

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

   if 6.0999999999999998e153 < 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 85.2%

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

   5. Simplified 85.2%

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

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

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

      2. sub0-neg N/A

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

      3. rec-exp N/A

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

      4. un-div-inv N/A

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

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

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

      6. exp-lowering-exp.f64 85.2%

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

   7. Applied egg-rr 85.2%

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

   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 85.2%

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

   10. Simplified 85.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + a \cdot \left(b \cdot 0.5\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 - b \cdot \left(-1 - b \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.4% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(b \cdot 0.16666666666666666 + 0.5\right)\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (* (* b (* b b)) -0.16666666666666666)) y)))
   (if (<= b -2.5e-5)
     t_1
     (if (<= b -5.2e-261)
       (/ (/ x (* a (+ 1.0 b))) y)
       (if (<= b 2.1e-108)
         t_1
         (/
          (/
           x
           (* a (+ 1.0 (* b (+ 1.0 (* b (+ (* b 0.16666666666666666) 0.5)))))))
          y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_1;
	} else if (b <= -5.2e-261) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 2.1e-108) {
		tmp = t_1;
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 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) :: t_1
    real(8) :: tmp
    t_1 = (x * ((b * (b * b)) * (-0.16666666666666666d0))) / y
    if (b <= (-2.5d-5)) then
        tmp = t_1
    else if (b <= (-5.2d-261)) then
        tmp = (x / (a * (1.0d0 + b))) / y
    else if (b <= 2.1d-108) then
        tmp = t_1
    else
        tmp = (x / (a * (1.0d0 + (b * (1.0d0 + (b * ((b * 0.16666666666666666d0) + 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 t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_1;
	} else if (b <= -5.2e-261) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 2.1e-108) {
		tmp = t_1;
	} else {
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y
	tmp = 0
	if b <= -2.5e-5:
		tmp = t_1
	elif b <= -5.2e-261:
		tmp = (x / (a * (1.0 + b))) / y
	elif b <= 2.1e-108:
		tmp = t_1
	else:
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(Float64(b * Float64(b * b)) * -0.16666666666666666)) / y)
	tmp = 0.0
	if (b <= -2.5e-5)
		tmp = t_1;
	elseif (b <= -5.2e-261)
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	elseif (b <= 2.1e-108)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * Float64(Float64(b * 0.16666666666666666) + 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	tmp = 0.0;
	if (b <= -2.5e-5)
		tmp = t_1;
	elseif (b <= -5.2e-261)
		tmp = (x / (a * (1.0 + b))) / y;
	elseif (b <= 2.1e-108)
		tmp = t_1;
	else
		tmp = (x / (a * (1.0 + (b * (1.0 + (b * ((b * 0.16666666666666666) + 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.5e-5], t$95$1, If[LessEqual[b, -5.2e-261], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.1e-108], t$95$1, N[(N[(x / N[(a * N[(1.0 + N[(b * N[(1.0 + N[(b * N[(N[(b * 0.16666666666666666), $MachinePrecision] + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.50000000000000012e-5 or -5.2000000000000002e-261 < b < 2.0999999999999999e-108

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-*r* N/A

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

      9. distribute-rgt-out N/A

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

      10. +-commutative N/A

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

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

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

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

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 46.7%

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

   8. Simplified 46.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

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

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. *-commutative N/A

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

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

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

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

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

       11. cube-mult N/A

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

       12. unpow2 N/A

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

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

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

       14. unpow2 N/A

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

       15. *-lowering-*.f64 66.7%

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

   11. Simplified 66.7%

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

   if -2.50000000000000012e-5 < b < -5.2000000000000002e-261

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 47.0%

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

   8. Simplified 47.0%

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

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. distribute-rgt1-in N/A

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

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

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

       4. +-lowering-+.f64 47.0%

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

   11. Simplified 47.0%

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

   if 2.0999999999999999e-108 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

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

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

      3. exp-to-pow N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

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

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

      8. exp-lowering-exp.f64 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

      8. exp-lowering-exp.f64 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

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

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

       6. *-commutative N/A

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

       7. *-lowering-*.f64 64.5%

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

   11. Simplified 64.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b \cdot \left(1 + b \cdot \left(b \cdot 0.16666666666666666 + 0.5\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.4% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\frac{x \cdot 0.5 + \frac{\frac{x}{b} - x}{b}}{b} - x \cdot 0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e-77)
   (/
    (*
     (* b (* b b))
     (- (/ (+ (* x 0.5) (/ (- (/ x b) x) b)) b) (* x 0.16666666666666666)))
    y)
   (/
    1.0
    (/
     (*
      y
      (+ a (* b (+ a (* b (+ (* a (* b 0.16666666666666666)) (* a 0.5)))))))
     x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e-77) {
		tmp = ((b * (b * b)) * ((((x * 0.5) + (((x / b) - x) / b)) / b) - (x * 0.16666666666666666))) / y;
	} else {
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d-77)) then
        tmp = ((b * (b * b)) * ((((x * 0.5d0) + (((x / b) - x) / b)) / b) - (x * 0.16666666666666666d0))) / y
    else
        tmp = 1.0d0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666d0)) + (a * 0.5d0))))))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e-77) {
		tmp = ((b * (b * b)) * ((((x * 0.5) + (((x / b) - x) / b)) / b) - (x * 0.16666666666666666))) / y;
	} else {
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e-77:
		tmp = ((b * (b * b)) * ((((x * 0.5) + (((x / b) - x) / b)) / b) - (x * 0.16666666666666666))) / y
	else:
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e-77)
		tmp = Float64(Float64(Float64(b * Float64(b * b)) * Float64(Float64(Float64(Float64(x * 0.5) + Float64(Float64(Float64(x / b) - x) / b)) / b) - Float64(x * 0.16666666666666666))) / y);
	else
		tmp = Float64(1.0 / Float64(Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(a * Float64(b * 0.16666666666666666)) + Float64(a * 0.5))))))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e-77)
		tmp = ((b * (b * b)) * ((((x * 0.5) + (((x / b) - x) / b)) / b) - (x * 0.16666666666666666))) / y;
	else
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e-77], N[(N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x * 0.5), $MachinePrecision] + N[(N[(N[(x / b), $MachinePrecision] - x), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(a * N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.7999999999999998e-77

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 63.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 63.4%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left({b}^{3} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x + -1 \cdot \frac{x}{b}}{b} + \frac{1}{2} \cdot x}{b} + \frac{1}{6} \cdot x\right)\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot {b}^{3}\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x + -1 \cdot \frac{x}{b}}{b} + \frac{1}{2} \cdot x}{b} + \frac{1}{6} \cdot x\right)\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot \frac{-1 \cdot \frac{x + -1 \cdot \frac{x}{b}}{b} + \frac{1}{2} \cdot x}{b} + \frac{1}{6} \cdot x\right) \cdot \left(-1 \cdot {b}^{3}\right)\right), y\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot \frac{-1 \cdot \frac{x + -1 \cdot \frac{x}{b}}{b} + \frac{1}{2} \cdot x}{b} + \frac{1}{6} \cdot x\right), \left(-1 \cdot {b}^{3}\right)\right), y\right) \]

   11. Simplified 71.9%

       \[\leadsto \frac{\color{blue}{\left(x \cdot 0.16666666666666666 - \frac{x \cdot 0.5 - \frac{x - \frac{x}{b}}{b}}{b}\right) \cdot \left(-1 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}}{y} \]

   if -4.7999999999999998e-77 < b

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 70.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 70.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 56.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 58.2%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 58.2%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)}\right), x\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right), x\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right), x\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right), x\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right), x\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(a \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{1}{6}\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(\frac{1}{6} \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{6} \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(a \cdot \frac{1}{2}\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       13. *-lowering-*.f64 54.4%

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

   13. Simplified 54.4%

       \[\leadsto \frac{1}{\frac{y \cdot \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\left(b \cdot \left(b \cdot b\right)\right) \cdot \left(\frac{x \cdot 0.5 + \frac{\frac{x}{b} - x}{b}}{b} - x \cdot 0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.3% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e-5)
   (/ (* x (* (* b (* b b)) -0.16666666666666666)) y)
   (/
    1.0
    (/
     (*
      y
      (+ a (* b (+ a (* b (+ (* a (* b 0.16666666666666666)) (* a 0.5)))))))
     x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e-5) {
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	} else {
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.5d-5)) then
        tmp = (x * ((b * (b * b)) * (-0.16666666666666666d0))) / y
    else
        tmp = 1.0d0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666d0)) + (a * 0.5d0))))))) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e-5) {
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	} else {
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e-5:
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y
	else:
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e-5)
		tmp = Float64(Float64(x * Float64(Float64(b * Float64(b * b)) * -0.16666666666666666)) / y);
	else
		tmp = Float64(1.0 / Float64(Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(a * Float64(b * 0.16666666666666666)) + Float64(a * 0.5))))))) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e-5)
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	else
		tmp = 1.0 / ((y * (a + (b * (a + (b * ((a * (b * 0.16666666666666666)) + (a * 0.5))))))) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e-5], N[(N[(x * N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(a * N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000012e-5

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 74.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 74.8%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{3} \cdot x\right) \cdot \frac{-1}{6}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{3} \cdot \left(x \cdot \frac{-1}{6}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{3} \cdot \frac{-1}{6}\right) \cdot x\right), y\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3}\right)\right)\right), y\right) \]

       11. cube-mult N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 80.8%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   11. Simplified 80.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}} \]

   if -2.50000000000000012e-5 < b

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 69.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 69.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 54.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 54.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 55.6%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 55.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)}\right), x\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right), x\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right), x\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right), x\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right), x\right)\right) \]

       5. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(a \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{1}{6}\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(a \cdot \left(\frac{1}{6} \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{1}{6} \cdot b\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       10. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(\frac{1}{2} \cdot a\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       12. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \left(a \cdot \frac{1}{2}\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

       13. *-lowering-*.f64 52.1%

           \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{1}{6}\right)\right), \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right)\right)\right)\right)\right)\right), x\right)\right) \]

   13. Simplified 52.1%

       \[\leadsto \frac{1}{\frac{y \cdot \color{blue}{\left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot \left(a + b \cdot \left(a + b \cdot \left(a \cdot \left(b \cdot 0.16666666666666666\right) + a \cdot 0.5\right)\right)\right)}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ t_2 := \frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (+ 1.0 b))) y))
        (t_2 (/ (* x (* (* b (* b b)) -0.16666666666666666)) y)))
   (if (<= b -2.5e-5)
     t_2
     (if (<= b -3.7e-261) t_1 (if (<= b 6.5e-107) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * (1.0 + b))) / y;
	double t_2 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_2;
	} else if (b <= -3.7e-261) {
		tmp = t_1;
	} else if (b <= 6.5e-107) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / (a * (1.0d0 + b))) / y
    t_2 = (x * ((b * (b * b)) * (-0.16666666666666666d0))) / y
    if (b <= (-2.5d-5)) then
        tmp = t_2
    else if (b <= (-3.7d-261)) then
        tmp = t_1
    else if (b <= 6.5d-107) then
        tmp = t_2
    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 / (a * (1.0 + b))) / y;
	double t_2 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_2;
	} else if (b <= -3.7e-261) {
		tmp = t_1;
	} else if (b <= 6.5e-107) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * (1.0 + b))) / y
	t_2 = (x * ((b * (b * b)) * -0.16666666666666666)) / y
	tmp = 0
	if b <= -2.5e-5:
		tmp = t_2
	elif b <= -3.7e-261:
		tmp = t_1
	elif b <= 6.5e-107:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y)
	t_2 = Float64(Float64(x * Float64(Float64(b * Float64(b * b)) * -0.16666666666666666)) / y)
	tmp = 0.0
	if (b <= -2.5e-5)
		tmp = t_2;
	elseif (b <= -3.7e-261)
		tmp = t_1;
	elseif (b <= 6.5e-107)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * (1.0 + b))) / y;
	t_2 = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	tmp = 0.0;
	if (b <= -2.5e-5)
		tmp = t_2;
	elseif (b <= -3.7e-261)
		tmp = t_1;
	elseif (b <= 6.5e-107)
		tmp = t_2;
	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[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.5e-5], t$95$2, If[LessEqual[b, -3.7e-261], t$95$1, If[LessEqual[b, 6.5e-107], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000012e-5 or -3.7000000000000002e-261 < b < 6.5000000000000002e-107

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 55.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 55.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 46.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 46.7%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{3} \cdot x\right) \cdot \frac{-1}{6}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{3} \cdot \left(x \cdot \frac{-1}{6}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{3} \cdot \frac{-1}{6}\right) \cdot x\right), y\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3}\right)\right)\right), y\right) \]

       11. cube-mult N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 66.7%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   11. Simplified 66.7%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}} \]

   if -2.50000000000000012e-5 < b < -3.7000000000000002e-261 or 6.5000000000000002e-107 < b

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 70.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 70.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 63.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 63.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a + b \cdot a\right)\right), y\right) \]

       2. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(b + 1\right) \cdot a\right)\right), y\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(b + 1\right), a\right)\right), y\right) \]

       4. +-lowering-+.f64 43.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), a\right)\right), y\right) \]

   11. Simplified 43.1%

       \[\leadsto \frac{\frac{x}{\color{blue}{\left(b + 1\right) \cdot a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.4% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ t_2 := \frac{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (+ 1.0 b))) y)) (t_2 (/ (* x (* 0.5 (* b b))) y)))
   (if (<= b -2.5e-5)
     t_2
     (if (<= b -4.2e-261) t_1 (if (<= b 2.15e-217) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * (1.0 + b))) / y;
	double t_2 = (x * (0.5 * (b * b))) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_2;
	} else if (b <= -4.2e-261) {
		tmp = t_1;
	} else if (b <= 2.15e-217) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / (a * (1.0d0 + b))) / y
    t_2 = (x * (0.5d0 * (b * b))) / y
    if (b <= (-2.5d-5)) then
        tmp = t_2
    else if (b <= (-4.2d-261)) then
        tmp = t_1
    else if (b <= 2.15d-217) then
        tmp = t_2
    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 / (a * (1.0 + b))) / y;
	double t_2 = (x * (0.5 * (b * b))) / y;
	double tmp;
	if (b <= -2.5e-5) {
		tmp = t_2;
	} else if (b <= -4.2e-261) {
		tmp = t_1;
	} else if (b <= 2.15e-217) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * (1.0 + b))) / y
	t_2 = (x * (0.5 * (b * b))) / y
	tmp = 0
	if b <= -2.5e-5:
		tmp = t_2
	elif b <= -4.2e-261:
		tmp = t_1
	elif b <= 2.15e-217:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y)
	t_2 = Float64(Float64(x * Float64(0.5 * Float64(b * b))) / y)
	tmp = 0.0
	if (b <= -2.5e-5)
		tmp = t_2;
	elseif (b <= -4.2e-261)
		tmp = t_1;
	elseif (b <= 2.15e-217)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * (1.0 + b))) / y;
	t_2 = (x * (0.5 * (b * b))) / y;
	tmp = 0.0;
	if (b <= -2.5e-5)
		tmp = t_2;
	elseif (b <= -4.2e-261)
		tmp = t_1;
	elseif (b <= 2.15e-217)
		tmp = t_2;
	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[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -2.5e-5], t$95$2, If[LessEqual[b, -4.2e-261], t$95$1, If[LessEqual[b, 2.15e-217], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000012e-5 or -4.19999999999999991e-261 < b < 2.15000000000000011e-217

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. 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 66.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 66.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \left(\frac{1}{2} \cdot b\right) \cdot x\right)\right)\right), y\right) \]

      4. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 46.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 46.9%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(-1 + b \cdot 0.5\right)\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot {b}^{2}\right) \cdot \frac{1}{2}\right), y\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\left(b \cdot b\right) \cdot \frac{1}{2}\right)\right), y\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(b \cdot \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot b\right) \cdot b\right)\right), y\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), y\right) \]

       13. *-lowering-*.f64 65.4%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   11. Simplified 65.4%

       \[\leadsto \frac{\color{blue}{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}}{y} \]

   if -2.50000000000000012e-5 < b < -4.19999999999999991e-261 or 2.15000000000000011e-217 < b

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 68.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 68.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 59.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 59.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{\left(a + a \cdot b\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a + b \cdot a\right)\right), y\right) \]

       2. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(b + 1\right) \cdot a\right)\right), y\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(b + 1\right), a\right)\right), y\right) \]

       4. +-lowering-+.f64 41.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), a\right)\right), y\right) \]

   11. Simplified 41.8%

       \[\leadsto \frac{\frac{x}{\color{blue}{\left(b + 1\right) \cdot a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.7% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\frac{a \cdot \left(y \cdot \left(1 + b\right)\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 - b \cdot \left(-1 - b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e-5)
   (/ (* x (* (* b (* b b)) -0.16666666666666666)) y)
   (if (<= b 3.2e+48)
     (/ 1.0 (/ (* a (* y (+ 1.0 b))) x))
     (/ (/ 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-5) {
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	} else if (b <= 3.2e+48) {
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x);
	} 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-5)) then
        tmp = (x * ((b * (b * b)) * (-0.16666666666666666d0))) / y
    else if (b <= 3.2d+48) then
        tmp = 1.0d0 / ((a * (y * (1.0d0 + b))) / x)
    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-5) {
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	} else if (b <= 3.2e+48) {
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x);
	} 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-5:
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y
	elif b <= 3.2e+48:
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x)
	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-5)
		tmp = Float64(Float64(x * Float64(Float64(b * Float64(b * b)) * -0.16666666666666666)) / y);
	elseif (b <= 3.2e+48)
		tmp = Float64(1.0 / Float64(Float64(a * Float64(y * Float64(1.0 + b))) / x));
	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-5)
		tmp = (x * ((b * (b * b)) * -0.16666666666666666)) / y;
	elseif (b <= 3.2e+48)
		tmp = 1.0 / ((a * (y * (1.0 + b))) / x);
	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-5], N[(N[(x * N[(N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.2e+48], N[(1.0 / N[(N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $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 < -2.50000000000000012e-5

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right)\right)\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + -1 \cdot x\right)\right)\right), y\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), y\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right) - x\right)\right)\right), y\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{-1}{6} \cdot \left(b \cdot x\right) + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{-1}{6} \cdot b\right) \cdot x + \frac{1}{2} \cdot x\right)\right), x\right)\right)\right), y\right) \]

      9. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{-1}{6} \cdot b + \frac{1}{2}\right)\right)\right), x\right)\right)\right), y\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right)\right)\right), x\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(\frac{-1}{6} \cdot b\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(b \cdot \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 74.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \frac{-1}{6}\right)\right)\right)\right), x\right)\right)\right), y\right) \]

   8. Simplified 74.8%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right) - x\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{\frac{-1}{6} \cdot \left({b}^{3} \cdot x\right)}{\color{blue}{y}} \]

       2. *-commutative N/A

          \[\leadsto \frac{\left({b}^{3} \cdot x\right) \cdot \frac{-1}{6}}{y} \]

       3. associate-*r* N/A

          \[\leadsto \frac{{b}^{3} \cdot \left(x \cdot \frac{-1}{6}\right)}{y} \]

       4. *-commutative N/A

          \[\leadsto \frac{{b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)}{y} \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left({b}^{3} \cdot \left(\frac{-1}{6} \cdot x\right)\right), \color{blue}{y}\right) \]

       6. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{3} \cdot \frac{-1}{6}\right) \cdot x\right), y\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\frac{-1}{6} \cdot {b}^{3}\right) \cdot x\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{-1}{6} \cdot {b}^{3}\right)\right), y\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left({b}^{3}\right)\right)\right), y\right) \]

       11. cube-mult N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \left(b \cdot {b}^{2}\right)\right)\right), y\right) \]

       13. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right)\right), y\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       15. *-lowering-*.f64 80.8%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   11. Simplified 80.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-0.16666666666666666 \cdot \left(b \cdot \left(b \cdot b\right)\right)\right)}{y}} \]

   if -2.50000000000000012e-5 < b < 3.2000000000000001e48

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 70.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 70.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 39.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 39.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 41.1%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 41.1%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\left(a \cdot y + a \cdot \left(b \cdot y\right)\right)}, x\right)\right) \]
   12. Step-by-step derivation

       1. distribute-lft-out N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y + b \cdot y\right)\right), x\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y + b \cdot y\right)\right), x\right)\right) \]

       3. distribute-rgt1-in N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(\left(b + 1\right) \cdot y\right)\right), x\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(b + 1\right), y\right)\right), x\right)\right) \]

       5. +-lowering-+.f64 40.4%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, 1\right), y\right)\right), x\right)\right) \]

   13. Simplified 40.4%

       \[\leadsto \frac{1}{\frac{\color{blue}{a \cdot \left(\left(b + 1\right) \cdot y\right)}}{x}} \]

   if 3.2000000000000001e48 < 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 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      3. rec-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 82.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y}} \]

   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 66.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   10. Simplified 66.5%

       \[\leadsto \frac{\frac{x}{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot \left(\left(b \cdot \left(b \cdot b\right)\right) \cdot -0.16666666666666666\right)}{y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\frac{a \cdot \left(y \cdot \left(1 + b\right)\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 - b \cdot \left(-1 - b \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e-6)
   (/ (* x (* 0.5 (* b b))) y)
   (if (<= b 5.8e+52) (/ 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 <= -7.2e-6) {
		tmp = (x * (0.5 * (b * b))) / y;
	} else if (b <= 5.8e+52) {
		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 <= (-7.2d-6)) then
        tmp = (x * (0.5d0 * (b * b))) / y
    else if (b <= 5.8d+52) 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 <= -7.2e-6) {
		tmp = (x * (0.5 * (b * b))) / y;
	} else if (b <= 5.8e+52) {
		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 <= -7.2e-6:
		tmp = (x * (0.5 * (b * b))) / y
	elif b <= 5.8e+52:
		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 <= -7.2e-6)
		tmp = Float64(Float64(x * Float64(0.5 * Float64(b * b))) / y);
	elseif (b <= 5.8e+52)
		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 <= -7.2e-6)
		tmp = (x * (0.5 * (b * b))) / y;
	elseif (b <= 5.8e+52)
		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, -7.2e-6], N[(N[(x * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.8e+52], 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 < -7.19999999999999967e-6

   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 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \left(\frac{1}{2} \cdot b\right) \cdot x\right)\right)\right), y\right) \]

      4. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 63.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 63.3%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(-1 + b \cdot 0.5\right)\right)}}{y} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \left({b}^{2} \cdot x\right)\right)}, y\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left({b}^{2} \cdot x\right) \cdot \frac{1}{2}\right), y\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(x \cdot {b}^{2}\right) \cdot \frac{1}{2}\right), y\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left({b}^{2} \cdot \frac{1}{2}\right)\right), y\right) \]

       4. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(\left(b \cdot b\right) \cdot \frac{1}{2}\right)\right), y\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(b \cdot \left(b \cdot \frac{1}{2}\right)\right)\right), y\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)\right), y\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot b\right) \cdot b\right)\right), y\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot {b}^{2}\right)\right), y\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left({b}^{2}\right)\right)\right), y\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot b\right)\right)\right), y\right) \]

       13. *-lowering-*.f64 70.5%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, b\right)\right)\right), y\right) \]

   11. Simplified 70.5%

       \[\leadsto \frac{\color{blue}{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}}{y} \]

   if -7.19999999999999967e-6 < b < 5.8e52

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 70.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 70.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 39.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 39.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 41.1%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 41.1%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 39.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 5.8e52 < 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 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      3. rec-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 82.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y}} \]

   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 27.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 27.5%

       \[\leadsto \frac{\frac{x}{\color{blue}{b + 1}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\left(0.5 \cdot \left(b \cdot b\right)\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e-5)
   (* (* 0.5 (* b b)) (/ x y))
   (if (<= b 7e+50) (/ 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 <= -2.5e-5) {
		tmp = (0.5 * (b * b)) * (x / y);
	} else if (b <= 7e+50) {
		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 <= (-2.5d-5)) then
        tmp = (0.5d0 * (b * b)) * (x / y)
    else if (b <= 7d+50) 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 <= -2.5e-5) {
		tmp = (0.5 * (b * b)) * (x / y);
	} else if (b <= 7e+50) {
		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 <= -2.5e-5:
		tmp = (0.5 * (b * b)) * (x / y)
	elif b <= 7e+50:
		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 <= -2.5e-5)
		tmp = Float64(Float64(0.5 * Float64(b * b)) * Float64(x / y));
	elseif (b <= 7e+50)
		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 <= -2.5e-5)
		tmp = (0.5 * (b * b)) * (x / y);
	elseif (b <= 7e+50)
		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, -2.5e-5], N[(N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+50], 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 < -2.50000000000000012e-5

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 91.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   6. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x + b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)}, y\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \frac{1}{2} \cdot \left(b \cdot x\right)\right)\right)\right), y\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(-1 \cdot x + \left(\frac{1}{2} \cdot b\right) \cdot x\right)\right)\right), y\right) \]

      4. distribute-rgt-out N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(x \cdot \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b - 1\right)\right)\right)\right), y\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot b + -1\right)\right)\right)\right), y\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \left(-1 + \frac{1}{2} \cdot b\right)\right)\right)\right), y\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \left(\frac{1}{2} \cdot b\right)\right)\right)\right)\right), y\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \left(b \cdot \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

      14. *-lowering-*.f64 63.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(b, \frac{1}{2}\right)\right)\right)\right)\right), y\right) \]

   8. Simplified 63.3%

      \[\leadsto \frac{\color{blue}{x + b \cdot \left(x \cdot \left(-1 + b \cdot 0.5\right)\right)}}{y} \]

   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-/l* N/A

          \[\leadsto \frac{1}{2} \cdot \left({b}^{2} \cdot \color{blue}{\frac{x}{y}}\right) \]

       2. *-commutative N/A

          \[\leadsto \frac{1}{2} \cdot \left(\frac{x}{y} \cdot \color{blue}{{b}^{2}}\right) \]

       3. associate-*l* N/A

          \[\leadsto \left(\frac{1}{2} \cdot \frac{x}{y}\right) \cdot \color{blue}{{b}^{2}} \]

       4. *-commutative N/A

          \[\leadsto \left(\frac{x}{y} \cdot \frac{1}{2}\right) \cdot {\color{blue}{b}}^{2} \]

       5. associate-*l* N/A

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)} \]

       6. unpow2 N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{2} \cdot \left(b \cdot \color{blue}{b}\right)\right) \]

       7. associate-*r* N/A

          \[\leadsto \frac{x}{y} \cdot \left(\left(\frac{1}{2} \cdot b\right) \cdot \color{blue}{b}\right) \]

       8. *-commutative N/A

          \[\leadsto \frac{x}{y} \cdot \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot b\right)}\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(b \cdot \left(\frac{1}{2} \cdot b\right)\right)}\right) \]

       10. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(\frac{1}{2} \cdot b\right)\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\left(\frac{1}{2} \cdot b\right) \cdot \color{blue}{b}\right)\right) \]

       12. associate-*r* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{1}{2} \cdot \color{blue}{\left(b \cdot b\right)}\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{1}{2} \cdot {b}^{\color{blue}{2}}\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right) \]

       15. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right) \]

       16. *-lowering-*.f64 64.4%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right) \]

   11. Simplified 64.4%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)} \]

   if -2.50000000000000012e-5 < b < 7.00000000000000012e50

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 70.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 70.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 39.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 39.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 41.1%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 41.1%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 39.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Simplified 39.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 7.00000000000000012e50 < 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 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      3. rec-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 82.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y}} \]

   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 27.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 27.5%

       \[\leadsto \frac{\frac{x}{\color{blue}{b + 1}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\left(0.5 \cdot \left(b \cdot b\right)\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -65:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -65.0)
   (/ (* x (- 1.0 b)) y)
   (if (<= b 2.2e+52) (/ 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 <= -65.0) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 2.2e+52) {
		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 <= (-65.0d0)) then
        tmp = (x * (1.0d0 - b)) / y
    else if (b <= 2.2d+52) 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 <= -65.0) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 2.2e+52) {
		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 <= -65.0:
		tmp = (x * (1.0 - b)) / y
	elif b <= 2.2e+52:
		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 <= -65.0)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	elseif (b <= 2.2e+52)
		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 <= -65.0)
		tmp = (x * (1.0 - b)) / y;
	elseif (b <= 2.2e+52)
		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, -65.0], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.2e+52], 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 < -65

   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 92.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 92.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   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. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot b + 1\right) \cdot x\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + -1 \cdot b\right) \cdot x\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + -1 \cdot b\right), x\right), y\right) \]

      5. neg-mul-1 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 44.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 44.5%

      \[\leadsto \frac{\color{blue}{\left(1 - b\right) \cdot x}}{y} \]

   if -65 < b < 2.2e52

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 69.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 69.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 38.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 38.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 40.8%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 40.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 39.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Simplified 39.1%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 2.2e52 < 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 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{0 - b}\right), \color{blue}{y}\right) \]

      2. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot e^{\mathsf{neg}\left(b\right)}\right), y\right) \]

      3. rec-exp N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{e^{b}}\right), y\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{e^{b}}\right), y\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(e^{b}\right)\right), y\right) \]

      6. exp-lowering-exp.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(b\right)\right), y\right) \]

   7. Applied egg-rr 82.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y}} \]

   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 27.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(b, 1\right)\right), y\right) \]

   10. Simplified 27.5%

       \[\leadsto \frac{\frac{x}{\color{blue}{b + 1}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -65:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{1 + b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.5% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3100:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3100.0) (/ (* 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 <= -3100.0) {
		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 <= (-3100.0d0)) 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 <= -3100.0) {
		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 <= -3100.0:
		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 <= -3100.0)
		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 <= -3100.0)
		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, -3100.0], 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 < -3100

   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 92.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

   5. Simplified 92.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

   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. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot b + 1\right) \cdot x\right), y\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 + -1 \cdot b\right) \cdot x\right), y\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 + -1 \cdot b\right), x\right), y\right) \]

      5. neg-mul-1 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 44.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, b\right), x\right), y\right) \]

   8. Simplified 44.5%

      \[\leadsto \frac{\color{blue}{\left(1 - b\right) \cdot x}}{y} \]

   if -3100 < b

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 68.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 68.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 53.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 55.3%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 55.3%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 29.5%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Simplified 29.5%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3100:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.05 \cdot 10^{-249}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2.05e-249) (/ (/ x a) y) (/ 1.0 (/ (* y a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.05e-249) {
		tmp = (x / a) / y;
	} else {
		tmp = 1.0 / ((y * a) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 2.05d-249) then
        tmp = (x / a) / y
    else
        tmp = 1.0d0 / ((y * a) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.05e-249) {
		tmp = (x / a) / y;
	} else {
		tmp = 1.0 / ((y * a) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 2.05e-249:
		tmp = (x / a) / y
	else:
		tmp = 1.0 / ((y * a) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2.05e-249)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 2.05e-249)
		tmp = (x / a) / y;
	else
		tmp = 1.0 / ((y * a) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2.05e-249], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.05000000000000002e-249

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 68.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 68.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 67.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 67.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a}\right)}, y\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 33.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   11. Simplified 33.7%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 2.05000000000000002e-249 < t

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 75.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 62.2%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 62.2%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{a}\right), x\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 30.3%

       \[\leadsto \frac{1}{\frac{y \cdot \color{blue}{a}}{x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 31.0% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.2e-239) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.2e-239) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.2d-239)) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.2e-239) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.2e-239:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.2e-239)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.2e-239)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.2e-239], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.1999999999999997e-239

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 67.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 67.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 66.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 66.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{a}\right)}, y\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 35.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right) \]

   11. Simplified 35.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if -6.1999999999999997e-239 < t

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      3. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 73.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   5. Simplified 73.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

      8. exp-lowering-exp.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

   8. Simplified 61.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
   9. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

      13. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

      17. exp-lowering-exp.f64 64.0%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

   10. Applied egg-rr 64.0%

       \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

       2. *-lowering-*.f64 29.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Simplified 29.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 31.3% 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 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(e^{\log a \cdot \left(t - 1\right) - b}\right)}\right), y\right) \]
4. Step-by-step derivation

   1. exp-diff N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}\right)\right), y\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(e^{\log a \cdot \left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

   3. exp-to-pow N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left({a}^{\left(t - 1\right)}\right), \left(e^{b}\right)\right)\right), y\right) \]

   4. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t - 1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + \left(\mathsf{neg}\left(1\right)\right)\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \left(t + -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \left(e^{b}\right)\right)\right), y\right) \]

   8. exp-lowering-exp.f64 71.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{pow.f64}\left(a, \mathsf{+.f64}\left(t, -1\right)\right), \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

5. Simplified 71.6%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
7. Step-by-step derivation

   1. associate-/r* N/A

      \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

   2. *-commutative N/A

      \[\leadsto \frac{\frac{x}{a}}{e^{b} \cdot \color{blue}{y}} \]

   3. associate-/r* N/A

      \[\leadsto \frac{\frac{\frac{x}{a}}{e^{b}}}{\color{blue}{y}} \]

   4. associate-/r* N/A

      \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a \cdot e^{b}}\right), \color{blue}{y}\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(a \cdot e^{b}\right)\right), y\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), y\right) \]

   8. exp-lowering-exp.f64 63.5%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), y\right) \]

8. Simplified 63.5%

   \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot e^{b}}}{y}} \]
9. Step-by-step derivation

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{a \cdot e^{b}}}}} \]

   2. metadata-eval N/A

      \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{\frac{x}{a \cdot e^{b}}}\right)}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{\frac{x}{a \cdot e^{b}}}\right)\right) \]

   5. div-inv N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \color{blue}{\frac{1}{\frac{x}{a \cdot e^{b}}}}\right)\right) \]

   6. clear-num N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(y \cdot \frac{a \cdot e^{b}}{\color{blue}{x}}\right)\right) \]

   7. associate-*r/ N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(a \cdot e^{b}\right)}{\color{blue}{x}}\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{y \cdot \left(e^{b} \cdot a\right)}{x}\right)\right) \]

   9. associate-*r* N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\left(y \cdot e^{b}\right) \cdot a}{x}\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{a \cdot \left(y \cdot e^{b}\right)}{x}\right)\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot e^{b}\right)\right), \color{blue}{x}\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(y \cdot e^{b}\right) \cdot a\right), x\right)\right) \]

   13. associate-*r* N/A

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(e^{b} \cdot a\right)\right), x\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot e^{b}\right)\right), x\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot e^{b}\right)\right), x\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \left(e^{b}\right)\right)\right), x\right)\right) \]

   17. exp-lowering-exp.f64 64.6%

       \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, \mathsf{exp.f64}\left(b\right)\right)\right), x\right)\right) \]

10. Applied egg-rr 64.6%

    \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(a \cdot e^{b}\right)}{x}}} \]

11. Taylor expanded in b around 0

    \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
12. Step-by-step derivation

    1. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

    2. *-lowering-*.f64 30.1%

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

13. Simplified 30.1%

    \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

14. Final simplification 30.1%

    \[\leadsto \frac{x}{y \cdot a} \]
15. Add Preprocessing

Alternative 25: 16.9% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / x);
}

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 = 1.0d0 / (y / x)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / x);
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (y / x)

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (y / x);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. 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 53.2%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 53.2%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 14.9%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 14.9%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Step-by-step derivation

   1. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x}}} \]

   2. metadata-eval N/A

      \[\leadsto \frac{-1 \cdot -1}{\frac{\color{blue}{y}}{x}} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot -1\right), \color{blue}{\left(\frac{y}{x}\right)}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\color{blue}{y}}{x}\right)\right) \]

   5. /-lowering-/.f64 15.2%

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

10. Applied egg-rr 15.2%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
11. Add Preprocessing

Alternative 26: 16.7% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. 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 53.2%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{\_.f64}\left(0, b\right)\right)\right), y\right) \]

5. Simplified 53.2%

   \[\leadsto \frac{x \cdot e^{\color{blue}{0 - b}}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 14.9%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

8. Simplified 14.9%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer Target 1: 72.1% 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 2024160 
(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))